Answer:
see work below
Step-by-step explanation:
F(x) is the same thing as y
y = 2x-3
exchange x and y
x = 2y-3
solve for y this is how we find the inverse function
add 3 to each side
x+3 = 2y-3+3
x+3 = 2y
divid by 2
(x+3)/2 = 2y/2
(x+3)/2 = y
the inverse of F(x) is (x+3)/2
to show one function is the inverse of the other,plug that function into the inverse function. You should get x as the answer
We will plug F(x) into G(x)
G(x) = (x+3)/2
put (2x-3) in for x
G(x) = ((2x-3)+3)/2
simplify the numberator
(2x-3+3)/2
2x/2
simplify
x
Since we got x back out
F(x) and G(x) are inverses
