will you help me with these functions please? i really don't get it.... explaint too if you can!?

Question

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

find:

g^-1 (x)

g^-1(g(x))

f(g(x))

g(f(x))

f(3+h)-f(3)/h

f(f(x))

Answer 1

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

g^-1 (x) = 1/g(x) = 1/(2x+1)
Substitute what g(x) is into the equation

g^-1(g(x)) = 1/g(g(x)) = 1/(2(2x+1)+1) = 1 / (4x +3)
Start on the inside and work out

f(g(x)) = (2x+1)^2 -3 = 2x^2 +4x + 1 -3 = 2x^2 + 4x - 2
Again, start on the inside and work out

g(f(x))
g(x^2-3) = 2(x^2-3) + 1 = 2x^2 -5

f(3+h)-f(3)/h
(3+h)^2 - 3 - (3^2-3)/h =
9 + 6h + h^2 -3 - (9-3)/h =
6 + 6h + h^2 - 6/h =
h^2 + 6h + 6 - 6h^(-1)

f(f(x)) =
f(x^2-3) = (x^2-3)^2 - 3 =
x^4 - 6x^2 + 9 -3 =
x^4 - 6x^2 + 6