Easy questions. No need for an explanation. only answers assignment_10__2.7_.pdfassignment_11__2.8_.pdf2/11/2016

Find

Assignment 10 (2.7)

f

(x).

g

√25−x2x+2

Find the domain of

f

(x). (Enter your answer using interval notation.)

g

(−2,5]

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Assignment 10 (2.7)

2. –/8 pointsSPreCalc7 2.7.015.

Consider the following functions.

9

,

x

Find (f + g)(x).

f(x) =

g(x) =

11

x + 11

Find the domain of (f + g)(x). (Enter your answer using interval notation.)

Find (f − g)(x).

Find the domain of (f − g)(x). (Enter your answer using interval notation.)

Find (fg)(x).

Find the domain of (fg)(x). (Enter your answer using interval notation.)

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Find

Assignment 10 (2.7)

f

(x).

g

Find the domain of

f

(x). (Enter your answer using interval notation.)

g

3. –/2 pointsSPreCalc7 2.7.028.MI.

Use f(x) = 3x − 4 and g(x) = 5 − x2 to evaluate the expression.

(a)

f(f(2))

(b)

g(g(3))

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Assignment 10 (2.7)

4. –/2 pointsSPreCalc7 2.7.029.MI.

Use f(x) = 2x − 4 and g(x) = 5 − x2 to evaluate the expression.

(a)

(f

g)(−2)

(b)

(g

f)(−2)

5. –/1 pointsSPreCalc7 2.7.033.MI.

Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the

gridlines.)

f(g(0)) =

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Assignment 10 (2.7)

6. –/1 pointsSPreCalc7 2.7.036.MI.

Use the given graphs of f and g to evaluate the expression. (Assume that each point lies on the

gridlines.)

(f

g)(−2) =

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Assignment 10 (2.7)

7. –/8 pointsSPreCalc7 2.7.049.MI.

Consider the following functions.

f(x) = x2,

Find (f

g(x) = x + 1

g)(x).

Find the domain of (f

Find (g

f)(x).

Find the domain of (g

Find (f

g)(x). (Enter your answer using interval notation.)

f)(x). (Enter your answer using interval notation.)

f)(x).

Find the domain of (f

f)(x). (Enter your answer using interval notation.)

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Find (g

Assignment 10 (2.7)

g)(x).

Find the domain of (g

g)(x). (Enter your answer using interval notation.)

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Assignment 10 (2.7)

8. –/8 pointsSPreCalc7 2.7.055.MI.

Consider the following functions.

x

,

x+8

g)(x).

f(x) =

Find (f

Find the domain of (f

Find (g

g)(x). (Enter your answer using interval notation.)

f)(x).

Find the domain of (g

Find (f

g(x) = 3x − 8

f)(x). (Enter your answer using interval notation.)

f)(x).

Find the domain of (f

f)(x). (Enter your answer using interval notation.)

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Assignment 10 (2.7)

Find (g

g)(x).

Find the domain of (g

g)(x). (Enter your answer using interval notation.)

9. –/1 pointsSPreCalc7 2.7.059.

Find f

g

h.

f(x) = x − 2,

g(x) =

x,

h(x) = x − 2

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Assignment 10 (2.7)

10.–/1 pointsSPreCalc7 2.7.063.

Express the function F in the form f g. (Enter your answers as a commaseparated list. Use non

identity functions for f(x) and g(x).)

F(x) = (x − 7)8

(f(x), g(x)) =

11.–/1 pointsSPreCalc7 2.7.066.

Express the function G in the form f

g. (There is more than one correct answer. The function is

of the form y = f(g(x)). Use nonidentity functions for f(x) and g(x).)

G(x) =

1

x+9

(f(x), g(x)) =

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Assignment 10 (2.7)

12.–/4 pointsSPreCalc7 2.7.077.

A stone is dropped in a lake, creating a circular ripple that travels outward at a speed of 60 cm/s.

(a) Find a function g that models the radius as a function of time t, in seconds.

g(t) =

(b) Find a function f that models the area of the circle as a function of the radius r, in cm.

f(r) =

(c) Find f

f

g.

g=

What does this function represent?

This function represents the area of the ripple as a function of the radius.

This function represents time as a function of the area of the ripple.

This function represents the radius of the ripple as a function of time.

This function represents the radius of the ripple as a function of area.

This function represents the area of the ripple as a function of time.

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Assignment 10 (2.7)

13.–/1 pointsSPreCalc7 2.7.079.

A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of

9 cm/s. Express the surface area of the balloon as a function of time t (in seconds). (Let S(0) =

0.)

S(t) =

cm2

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Assignment 11 (2.8)

2. –/1 pointsSPreCalc7 2.8.009.

A graph of a function f is given.

Determine whether f is onetoone.

Yes, f is onetoone.

No, f is not onetoone.

3. –/1 pointsSPreCalc7 2.8.013.

Determine whether the function is onetoone.

f(x) = −7x + 4

is onetoone

is not onetoone

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Assignment 11 (2.8)

4. –/1 pointsSPreCalc7 2.8.017.

Determine whether the function is onetoone.

h(x) = x2 − 5x

is onetoone

is not onetoone

5. –/2 pointsSPreCalc7 2.8.026.MI.

Assume that f is a onetoone function.

(a) If f(5) = 15, find f −1(15).

f −1(15) =

(b) If f −1(30) = 15, find f(15).

f(15) =

6. –/1 pointsSPreCalc7 2.8.037.

Use the Inverse Function Property to determine whether f and g are inverses of each other.

f(x) = x − 9;

g(x) = x + 9

f and g are inverses of each other.

f and g are not inverses of each other.

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Assignment 11 (2.8)

7. –/1 pointsSPreCalc7 2.8.045.

Use the Inverse Function Property to determine whether f and g are inverses of each other.

1

1

, x ≠ 10; g(x) =

+ 10

x − 10

x

f and g are inverses of each other.

f(x) =

f and g are not inverses of each other.

8. –/1 pointsSPreCalc7 2.8.052.

Find the inverse function of f.

f(x) = 2×3 + 4

f −1(x) =

9. –/1 pointsSPreCalc7 2.8.055.

Find the inverse function of f.

f(x) =

x

x+5

f −1(x) =

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Assignment 11 (2.8)

10.–/1 pointsSPreCalc7 2.8.067.MI.

Find the inverse function of f.

f(x) =

3 + 8x

f −1(x) =

,

x≥0

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Assignment 11 (2.8)

11.–/2 pointsSPreCalc7 2.8.086.

The given function is not onetoone.

g(x) = (x − 4)2

Restrict its domain so that the resulting function is onetoone.

[3, ∞)

(−∞, 5]

(−∞, ∞)

[4, ∞)

(−5, ∞)

Find the inverse of the function with the restricted domain above.

g−1(x) =

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Assignment 11 (2.8)

12.–/1 pointsSPreCalc7 2.8.089.

Use the graph of f to sketch the graph of f −1.

Graph f −1 using closed endpoints for each segment.

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Assignment 11 (2.8)

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Assignment 11 (2.8)

13.–/5 pointsSPreCalc7 2.8.094.MI.

For his services, a private investigator requires a $550 retainer fee plus $80 per hour. Let x

represent the number of hours the investigator spends working on a case.

(a) Find a function f that models the investigator’s fee as a function of x.

f(x) =

(b) Find f −1.

f −1(x) =

What does f −1 represent?

f −1 represents the amount in dollars paid for x numbers of hours of investigation.

f −1 represents the amount in dollars paid beyond the retention fee for x numbers of

hours of investigation.

f −1 represents the number of hours of investigation the investigator spends on a

case for x dollars.

f −1 represents the maximum number of hours of investigation the investigator will

spend on a case.

f −1 represents the amount paid per each hour of investigation.

(c) Find f −1(1270).

f −1(1270) =

What does your answer represent?

f −1(1270) represents the amount in dollars paid for 1270 hours of investigation.

f −1(1270) represents the amount in dollars paid beyond the retention fee for 1270

hours of investigation.

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Assignment 11 (2.8)

f −1(1270) represents the number of hours of investigation the investigator spends

on a case for $1270.

f −1(1270) represents the maximum number of hours of investigation the

investigator will spend on a case.

f −1(1270) represents the amount paid per each hour of investigation.

14.–/1 pointsSPreCalc7 2.8.507.XP.

Find the inverse function of f.

f(x) =

9x − 1

x−2

f −1(x) =

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1.

-/1 points SPreCalc7 2.8.007.

My Notes

A graph of a function fis given.

y

х

0

Determine whether fis one-to-one.

Yes, f is one-to-one.

No, f is not one-to-one.

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