The function f is defined by f(x) = 4x - 9. The function g is... | SAT Linear functions Question, Answer Explained

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The function $f$ is defined by $f(x) = 4x - 9$ . The function $g$ is defined by $g(x) = f(x + 2)$ . Which equation defines $g$ ?

$g(x) = 4x - 17$

$g(x) = 4x - 7$

$g(x) = 4x - 1$

$g(x) = 6x - 9$

Show answer and explanation

Answer: C

Replace $x$ with $x + 2$ in the definition of $f$ : $g(x) = 4(x + 2) - 9 = 4x + 8 - 9 = 4x - 1$ .

Choice B adds $2$ to the output, $f(x) + 2$ , instead of to the input.

Why the other choices are wrong

A. This is f(x - 2) = 4(x - 2) - 9. The function g adds 2 to the input; it doesn't subtract 2.
B. This is f(x) + 2, which adds 2 to the output of f instead of to its input.
D. This adds 2 to the coefficient of x. The 4 must multiply the whole input, x + 2.

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