QuestionEvaluate the function $g(x)=4x+1$ for: (a) $g(-4)$ , (b) $g(a)$ , (c) $g(x^{3})$ , (d) $g(4x-3)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $g(x) =4x +1$ . We need to evaluate the function at different values or expressions of $x$

STEP 2

To evaluate the function $g(x)$ at a certain value or expression, we replace $x$ in the function with that value or expression.

STEP 3

For part (a), we need to evaluate $g(-)$ . So, we replace $x$ in the function $g(x)$ with $-$ .
$g(-) =(-) +1$

STEP 4

Calculate the value of $g(-4)$ .
$g(-4) =4(-4) +1 = -16 +1 = -15$ So, $g(-4) = -15$ .

STEP 5

For part (b), we need to evaluate $g(a)$ . So, we replace $x$ in the function $g(x)$ with $a$ .
$g(a) =4a +1$ So, $g(a) =4a +1$ .

STEP 6

For part (c), we need to evaluate $g\left(x^{3}\right)$ . So, we replace $x$ in the function $g(x)$ with $x^{3}$ .
$g\left(x^{3}\right) =4x^{3} +1$ So, $g\left(x^{3}\right) =4x^{3} +1$ .

STEP 7

For part (d), we need to evaluate $g(4x -3)$ . So, we replace $x$ in the function $g(x)$ with $4x -3$ .
$g(4x -3) =4(4x -3) +1$

STEP 8

Calculate the value of $g(4x -3)$ .
$g(4x -3) =4(4x -3) +1 =16x -12 +1 =16x -11$ So, $g(4x -3) =16x -11$ .
The solutions are(a) $g(-4) = -15$ (b) $g(a) =4a +1$ (c) $g\left(x^{3}\right) =4x^{3} +1$ (d) $g(4x -3) =16x -11$

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