Verify that f and g are inverse functions.

Question

Verify that f and g are inverse functions.

 

1.  f(x) = 2x +5, g(x) = x-5/2

 

2.  f(x) = ^{3√x, g(x) =} x³

 

If you could please help me out on these problems I would really appreciate it. Thank you so much.

Answer 1

1)

 

First, switch places with x and y.  where y=f(x).

 

x = 2y + 5

 

 

Solve for y.  The value of y obtained here is the inverse.

 

x - 5 = 2y

 

(x - 5) / 2 = y

 

(x - 5) / 2 = g(x)

 

 

f(x) and g(x) are inverses.

 

 

2)

 

Do the same procedure.

 

x = ³√y   ---->  this is read as the cube-root of y

 

 

Solving for y,

 

x³ = y

 

x³ = g(x)

 

 

The functions are inverses.