The functions f and g are defined for all real numbers by f(x) = 2x - 5 and g(x) = (x + 3)… — ACT

The functions $f$ and $g$ are defined for all real numbers by $f(x) = 2x - 5$ and $g(x) = (x + 3)^2$ . What is the value of $f(g(-1))$ ?

To evaluate the composite function

f(g(-1))

, first evaluate the inner function

g(-1) = (-1 + 3)^2 = 4

. Then, substitute this result into the outer function to get

f(4) = 2(4) - 5 = 3

Evaluate the inner function

g(x)

x = -1

g(-1) = 4

In the composition

f(g(-1))

, the inner function must be evaluated first. Substituting

-1

into

g(x) = (x + 3)^2

gives

g(-1) = (-1 + 3)^2 = 2^2 = 4

Evaluate the outer function

f(x)

at the output of the inner function.

f(4) = 3

Substitute the output

g(-1) = 4

into

f(x) = 2x - 5

, which yields

f(4) = 2(4) - 5 = 8 - 5 = 3

Function Composition and Evaluation

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