For all real numbers x such that x \neq 1, the function f is defined by f(x) = \frac{12}{x… — ACT

For all real numbers $x$ such that $x \neq 1$ , the function $f$ is defined by $f(x) = \frac{12}{x - 1}$ . For all real numbers $x$ , the function $g$ is defined by $g(x) = x^2 + 2$ . What is the value of the composite function $f(g(3))$ ?

Answer: 1.2

Answer

1.2

To evaluate the composite function

f(g(3))

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

g(3) = 3^2 + 2 = 11

. Next, substitute this result into the outer function

f(x)

to get

f(11) = \frac{12}{11 - 1} = \frac{12}{10} = 1.2

Step-by-Step Solution

Evaluate the inner function

g(x)

x = 3

g(3) = 11

To evaluate a composite function of the form

f(g(x))

at a given value, we must first find the output of the inner function,

g(x)

, at that value.

Substitute the output from Step 1 as the input for the outer function

f(x)

and evaluate.

f(g(3)) = 1.2

Using the result

g(3) = 11

as the input for

f(x)

gives

f(11) = \frac{12}{11 - 1} = 1.2

Key Concept

Function Composition and Evaluation

Question

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Step-by-Step Solution

Key Concept

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