Final answer:
Using the concept of composition of functions will get the inverse of F(x) is 2x – 3.
Step-by-step explanation:
To show that g(X)= x+3/2 is the inverse of F(x) = 2x – 3, we can use the concept of composition of functions.
The composition of F(g(x)) should give us x and the composition of g(F(x)) should also give us x.
Let's calculate the composition of F(g(x)):
1) Start with F(g(x)) = 2(g(x)) – 3
2) Replace g(x) with x+3/2:
F(g(x)) = 2((x+3/2)) – 3
3) Simplify: F(g(x)) = 2x + 3 – 3
= 2x
Since we obtained x as the result, we can conclude that g(x) = x+3/2 is the inverse of F(x) = 2x – 3.