QuestionEvaluate $g(x)=3 x^{2}-5$ for: (a) $g(-4)$ , (b) $g(b)$ , (c) $g(x^{3})$ , (d) $g(3 x-4)$ .

Studdy Solution

STEP 1

Assumptions1. The function $g(x)$ is defined as $g(x) =3x^{} -5$ . We are asked to evaluate $g(x)$ for four different inputs $-4$ , $b$ , $x^{3}$ , and $3x-4$

STEP 2

To evaluate the function $g(x)$ at a particular value, we substitute that value in place of $x$ in the function definition.
(a) For $g(-4)$ , we substitute $-4$ in place of $x$ in the function definition.
$g(-4) =(-4)^{2} -5$

STEP 3

Calculate the value of $g(-)$ .
$g(-) =3 \cdot16 -5 =48 -5 =43$ (b) For $g(b)$ , we substitute $b$ in place of $x$ in the function definition.
$g(b) =3b^{2} -5$

STEP 4

The expression $g(b) =3b^{2} -$ is already simplified, so we don't need to do any further calculations. The correct choice is A. $g(b)=3 b^{2}-$ .
(c) For $g\left(x^{3}\right)$ , we substitute $x^{3}$ in place of $x$ in the function definition.
$g\left(x^{3}\right) =3(x^{3})^{2} -$

STEP 5

Calculate the value of $g\left(x^{3}\right)$ .
$g\left(x^{3}\right) =3x^{} -5$ The correct choice is A. $g\left(x^{3}\right)=3 x^{}-5$ .
(d) For $g(3x-4)$ , we substitute $3x-4$ in place of $x$ in the function definition.
$g(3x-4) =3(3x-4)^{2} -5$

STEP 6

Expand the expression $g(3x-4)$ .
$g(3x-4) =3(9x^{2} -24x +16) -5$

STEP 7

implify the expression $g(3x-4)$ .
$g(3x-4) =27x^{2} -72x +48 -5 =27x^{2} -72x +43$ The correct choice is A. $g(3x-4) =27x^{2} -72x +43$ .

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