if f(x) = x + 1 and g(x) = 2x^2 - 3?

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

In the function f(x) substitute x with the function g(x) = 2x^2 - 3
f(g(x)) = (2x^2 - 3) + 1

Now, just simplify
f(g(x)) = 2x^2 - 2

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

to find f of g of x, put g(x) into equation for f(x)

f(x)= g(x) +1

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

f(g(x))=2x^2-2

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

That notation means to take g(x) and put it in for x in the f(x) equation.

So in f(x) = x + 1, I am going to throw out the x and put in 2x^2 - 3

{f o g}(x) = 2x^2 - 3 +1

Simplify.

{f o g}(x) = 2x^2 - 2

substitute the g(x) into the equation of f(x)
[f of g](x)=(2x^2 - 3)+1
=2x^2 - 2

f(g(x))=2x^2-2