Question

If f(x)=x²-2 and g(x)=x-3, what is (fog)(x)?

O (fog)(x) = x² +7
(fog)(x)=x²-6x+7
O (fog)(x)=x²-3x+7
O (fog)(x)=x²-5

Answer 1

The correct answer is (fog)(x) = x² - 6x + 7.

To evaluate (fog)(x), you first need to find g(x) and then substitute the result into f(x).

g(x) = x - 3

So, (fog)(x) = f(g(x)) = f(x - 3) = (x - 3)² - 2 = x² - 6x + 9 - 2 = x² - 6x + 7.

I hope this helps! Let me know if you have any other questions.

Explanation:

SELF EXPLANATORY

Answer 2

`(f \circ g)(x)=x^2-6x+7`

Explanation:

Given functions:

`\begin{cases}f(x)=x^2-2\\g(x)=x-3\end{cases}`

Function composition is an operation that takes two functions and produces a third function.

The given composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x):

`\begin{aligned}(f \circ g)(x)&=[g(x)]^2-2\\&=(x-3)^2-2\\&=x^2-6x+9-2\\&=x^2-6x+7\end{aligned}`