Question

Prove that f(x)=x+3/2 and g(x)=2x-3are inverse

I Really Need This Answer Please!!!!!!!!!

Answer 1

See proof below.

Explanation:

Note:

I think you mean that f(x) = (x + 3)/2, which is
`f(x) = (x + 3)/(2)` and not what you wrote which means
`f(x) = x + (3)/(2)`

To prove that functions f(x) and g(x) are inverses of each other, you must do the composition of functions f and g, and then the composition of functions g and f. If both compositions give you the result of just x, then the functions are inverses of each other.

`f(x) = (x + 3)/(2); g(x) = 2x - 3`

`(f \circ g)(x) = f(g(x)) = (g(x) + 3)/(2) = (2x - 3 + 3)/(2) = (2x)/(2) = x`

`(g \circ f)(x) = g(f(x)) = 2(f(x)) - 3 = (2(x + 3))/(2) - 3 = x + 3 - 3 = x`

Since both compositions result in x, functions f(x) and g(x) are proved to be inverses of each other.