For the functions f(x) = (x - 2)^2 - 5 and g(x) = |x + 1| - 3, what is the value of f(g(-2… — ACT

For the functions $f(x) = (x - 2)^2 - 5$ and $g(x) = |x + 1| - 3$ , what is the value of $f(g(-2))$ ?

To find the value of

f(g(-2))

, first evaluate the inner function

g(x)

x = -2

. Substituting

-2

into

g(x) = |x + 1| - 3

gives

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

. Next, substitute this output as the input for the outer function

f(x)

. Substituting

-2

into

f(x) = (x - 2)^2 - 5

yields

f(-2) = (-2 - 2)^2 - 5 = (-4)^2 - 5 = 16 - 5 = 11

Evaluate the inner function at the given input value

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

In function composition

f(g(x))

, the inner function must be evaluated first to determine the input for the outer function.

Evaluate the outer function using the output of the inner function

f(-2) = (-2 - 2)^2 - 5 = (-4)^2 - 5 = 16 - 5 = 11

Substitute the result from the inner function evaluation into the outer function to find the final value.

Function composition and evaluation

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