Let the functions f and g be defined by f(x) = (x - 3)^2 and g(x) = 2x + 1. What is the va… — ACT

Let the functions $f$ and $g$ be defined by $f(x) = (x - 3)^2$ and $g(x) = 2x + 1$ . What is the value of the composite function $f(g(-2))$ ?

Answer: 36

To evaluate the composite function

f(g(-2))

, evaluate from the inside out. First, evaluate the inner function

g(-2) = 2(-2) + 1 = -3

. Next, substitute this output value into the outer function

f(x)

to get

f(-3) = (-3 - 3)^2 = (-6)^2 = 36

Evaluate the inner function

g(x)

x = -2

g(-2) = -3

Before evaluating the outer function

f

, we must determine the output of the inner function

g

at the given input value.

Evaluate the outer function

f(x)

at the result of the inner function

f(-3) = 36

Substitute the inner output

-3

as the input for

f(x) = (x - 3)^2

, giving

(-3 - 3)^2 = (-6)^2 = 36

Function composition and evaluation

Estimated Time:1m 0s

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