g(x)=(2x−5)^3 and h(x)= square root cubed of x +5/2

Question

are functions g(h(x)) and h(g(x)) inverses?

Answer 1

First, I suggest that you graph the two equations given.

2 functions which are inverses will be symmetric with respect to the line y = x.

 

Second to compute the inverse of g(x), write y = (2x-5)³ and then exchanges the roles of x and y, i.e.

x = (2y-5)³ and solve for y

 

x^1/3 = 2y - 5 => x^1/3 + 5 = 2y and y = (1/2)(x^1/3 + 5)

 

Now add this function to your graph and look at the relation between this function and g(x)!