Inverse of a Function Answers

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Consider the graph shown. Which ordered pairs are on the inverse of the function? Check all that apply.

(–5, –2)

(0, –1)

(0, 1)

(–1, 0)

(1, 0)

(4, 1)

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Answer:

160/9

166112

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Answer:

166115

Complete the statements to verify that f(x) = 10x and g(x) = log10x are inverses of each other.

Answers:

Using the law of logarithms blogbn = , we have that f(g(x)) = .:n

Using the law of logarithms blogbn = , we have that f(g(x)) = .:x

We also need to show that is also equal to x.:g(f(x))

Using the law of logarithms logbbn = , which means that g(f(x)) = x.:n

166116

✔ x10xlog(x)log(10x)

✔ x

10x

log(x)

log(10x)

166117

f(g(–x))(f + g)(x)(g – f)(x)✔ g(f(x))

f(g(–x))

(f + g)(x)

(g – f)(x)

✔ g(f(x))

166118

b✔ nlog(b)log(n)

✔ n

log(b)

log(n)

166119

Find the following values of the function. f -1 = f -1 (8) =

Answers:

Part 1:2

Part 2:6

166120

Consider the function show. Explain why the graph of a function and its inverse are reflections over the line y = x.

The ordered pairs (a, b) of a function are (–a, –b) for the inverse function.

The ordered pairs (a, b) of a function are (–b, –a) for the inverse function.

The ordered pairs (a, b) of a function are (a, b) for the inverse function.

The ordered pairs (a, b) of a function are (b, a) for the inverse function.

166121

Given the function f(x) = 4x, which statements are true? Check all that apply.

The additive inverse is –4x.

The additive inverse is 4x.

The multiplicative inverse is .

The multiplicative inverse is .

f Superscript negative 1 Baseline (x) = negative one-fourth x

f Superscript negative 1 Baseline (x) = one-fourth x

166122

What is the inverse function of g(x)?

g–1(x) = – 2x – 3

g–1(x) = – 3(x – 3)

g–1(x) = – 3x – 2

g–1(x) = – 2(x – 3)

166123

What is the inverse function of f(x)?

, x ≥ 0

, x ≥ -2

f –1(x) = – 6x2 – 3, x ≥ –0

f –1(x) = – 3x2 – 6, x ≥ -2

166124

Consider the function shown. How can you restrict the domain so that f(x) has an inverse? What is the equation of the inverse function?

x > –2;

x > 2;

166125

If f(x) = 6x – 1 and , which expressions can be used to verify g(x) is the inverse of f(x)? Check all that apply.

6(6x – 1) – 1

StartFraction (6 x minus 1) + 1 Over 6 EndFraction

StartStartFraction (StartFraction x + 1 Over 6 EndFraction) + 1 OverOver 6 EndEndFraction

StartFraction x + 1 Over 6 EndFraction + 6 x minus 1

166126

The formula for converting a temperature in degrees Celsius to degrees Fahrenheit is F(C)= C + 32. The inverse function will convert a temperature in degrees Fahrenheit to degrees Celsius. What is the formula for converting from degrees Fahrenheit to degrees Celsius? C(F) = F – .

Answers:

Part 1:5/9

Part 2:166114

166127

Complete the statements to verify that f(x) = 10x and g(x) = log10x are inverses of each other.

Answers:

Using the law of logarithms blogbn = , we have that f(g(x)) = .:n

Using the law of logarithms blogbn = , we have that f(g(x)) = .:x

We also need to show that is also equal to x.:g(f(x))

Using the law of logarithms logbbn = , which means that g(f(x)) = x.:n

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