Question

Difficulty: MediumFunction Evaluation, Composition, and Properties

Given the functions $f(x) = \sqrt{3x + 4}$ and $g(x) = x^2 - 5$ , what is the value of $g(f(7))$ ?

Answer: 20

Evaluating the inner function first gives

f(7) = \sqrt{3(7) + 4} = 5

. Substituting this value into the outer function yields

g(5) = 5^2 - 5 = 20

Evaluate the inner function

f(x)

x = 7

f(7) = 5

To evaluate a composite function of the form

g(f(x))

, we first calculate the value of the inner function

f(x)

at the given input.

Substitute the output of the inner function as the input for the outer function

g(x)

g(5) = 20

Since

f(7) = 5

, evaluating

g(f(7))

is equivalent to evaluating

g(5)

Function composition involves evaluating an inner function and then using that result as the input for an outer function.

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