Question

Difficulty: MediumFunction Evaluation, Composition, and Properties

For the functions $f(x) = \frac{18}{x - 2}$ and $g(x) = x^2 - 1$ , what is the value of $f(g(3))$ ?

Answer: 3

The value of the composite function

f(g(3))

is 3.

To evaluate the composite function

f(g(3))

, we start by evaluating the inner function

g(3) = 3^2 - 1 = 8

. We then substitute this result into the outer function, giving

f(8) = \frac{18}{8 - 2} = \frac{18}{6} = 3

Evaluate the inner function

g(3)

For any composite function of the form

f(g(x))

, the inner function

g(x)

must be evaluated first at the given input value.

Evaluate the outer function

f(8)

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

f(x)

Function Composition and Evaluation

Estimated Time:1m 0s

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