Question

Given: f(x)=x²-3 and g(x)=x+1. What is the composite function gOf?

1. x²+2x-2

2. x²+2x-2

3. x²-2

Answer 1

gOf = g(f(x))
so
g(f(x)) = (x^2 - 3) + 1
g(f(x)) = x^2 - 2

answer

3. x²-2

Answer 2

For two given functions f(x) and g(x), the composite function

(g ° f)(x) is: g(f(x))

Here we will find that the correct option is the last one:

(g°f)(x) = x²-2

To get this, we know that:

g(x) = x + 1

f(x) = x² - 3

Then:

(g°f)(x) = g(f(x))

So here we just need to evaluate g(x) in f(x):

g(f(x)) = f(x) + 1 = ( x² - 3) + 1 = x² - 3 + 1 = x² - 2

Then the correct option is 3:

(g°f)(x) = x²-2

If you want to learn more, you can read:

https://brainly.com/question/5614233