Question

Difficulty: MediumFunction Evaluation, Composition, and Properties

For the functions $f(x) = |4x - 17|$ and $g(x) = 3 - 2x$ , what is the value of $f(g(5))$ ?

Answer: 45

The correct answer is 45.

Evaluating the inner function first yields

g(5) = 3 - 2(5) = -7

. Substituting this result into the outer function gives

f(-7) = |4(-7) - 17| = |-45| = 45

Evaluate the inner function

g(5)

g(5) = 3 - 2(5) = -7

In a composite function of the form

f(g(x))

, the inner function

g(x)

must be evaluated first at the given input.

Evaluate the outer function

f(x)

at the output of the inner function

f(-7) = |4(-7) - 17| = |-28 - 17| = |-45| = 45

The output of the inner function,

-7

, becomes the input for the outer function

f(x)

Function Evaluation and Composition

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