QuestionDiketahui $(f \circ g)(x)=x^{2}+2 x-3$ dan $f(x)=x+3$ . Temukan $g(x)$ dan nilai $g(-2)$ .

Studdy Solution

STEP 1

Assumptions1. The composite function $(f \circ g)(x)=x^{}+ x-3$ is given. . The function $f(x)=x+3$ is given.
3. We need to find the function $g(x)$ and the value of $g(-)$ .

STEP 2

First, we need to express the composite function $(f \circ g)(x)$ in terms of $f$ and $g$ . The composite function is defined as $(f \circ g)(x) = f(g(x))$ .

STEP 3

Now, we know that $f(x)=x+3$ . We can substitute $f(g(x))$ with $g(x)+3$ in the equation $(f \circ g)(x)=x^{2}+2 x-3$ .
$g(x)+3 = x^{2}+2 x-3$

STEP 4

To find the function $g(x)$ , we need to isolate $g(x)$ in the equation. So, we subtract3 from both sides of the equation.
$g(x) = x^{2}+2 x-3 -3$

STEP 5

implify the right side of the equation to get the function $g(x)$ .
$g(x) = x^{2}+2 x-$

STEP 6

Now that we have the function $g(x)$ , we can find the value of $g(-2)$ by substituting $x$ with $-2$ in the function.
$g(-2) = (-2)^{2}+2(-2)-6$

STEP 7

implify the right side of the equation to get the value of $g(-2)$ .
$g(-2) =4-4-6$

STEP 8

Calculate the value of $g(-2)$ .
$g(-2) = -6$ So, the function $g(x) = x^{2}+2 x-6$ and the value of $g(-2)$ is -6.

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