Question

Difficulty: EasyFunction Evaluation, Composition, and Properties

Let the functions $f$ and $g$ be defined for all real numbers by $f(x) = 2x - 3$ and $g(x) = x + 5$ . What is the value of $f(g(4))$ ?

Answer: 15

The value of

f(g(4))

15

To evaluate the composite function

f(g(4))

, the inner function must be evaluated first. Substituting

4

into

g(x) = x + 5

gives

g(4) = 9

. Next, substitute this output of

9

into the outer function

f(x) = 2x - 3

, which gives

f(9) = 2(9) - 3 = 15

Evaluate the inner function

g(4)

g(4) = 9

Substitute

4

for

x

in the definition of

g(x) = x + 5

Evaluate the outer function

f(x)

at the output of the inner function

f(9) = 15

Substitute

9

(the value of

g(4)

) for

x

in the definition of

f(x) = 2x - 3

Function Composition and Evaluation

Estimated Time:45s

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