For all real numbers x, the function f is defined by f(x) = 3 - x^2. For all real numbers … — GRE General Test

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

$\frac{13}{4}$ Answer
B
$\frac{23}{14}$
C
$-46$
D
$-42$
E
$-\frac{1}{2}$

Answer

The correct answer is

\frac{13}{4}

First, evaluate the inner expression

f(-3) = 3 - (-3)^2 = 3 - 9 = -6

. Next, evaluate the outer expression at this value:

g(-6) = \frac{2(-6) - 1}{-6 + 2} = \frac{-13}{-4} = \frac{13}{4}

Step-by-Step Solution

Evaluate the inner function

f(-3)

f(-3) = 3 - (-3)^2 = 3 - 9 = -6

Applying the definition of

f(x)

where the negative base is squared to yield positive

9

Substitute the result into the outer function

g(x)

g(-6) = \frac{2(-6) - 1}{-6 + 2} = \frac{-12 - 1}{-4} = \frac{-13}{-4} = \frac{13}{4}

Evaluating

g(x)

x = -6

and simplifying the fraction.

Key Concept

Nested Function Evaluation

g(f(x))

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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