Show that g(X)= x+3/2 is the inverse of F(x) = 2x – 3. Write your answer in inverse notation.

Question

asked Jan 17, 2024 154k views

1 Answer

Wdavo · Answer 1 · 2024-01-23T13:24:58+0000

Using the concept of composition of functions will get the inverse of F(x) is 2x – 3.

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.