what is the inverse of the fuctions 3x-2 and f(x)=x^3

Question

looking for some school help, need to know the inverse function of the function f(x)=3x-2 also f(x)=x^3

Answer 1

Here is the procedure, so you can always figure out the inverse yourself.

 

Assume y = f(x) = 3x-2. 

(test it to make sure it can have an inverse, i.e. it must be strictly increasing or strictly decreasing).

 

Rewrite, exchanging letters x & y:  You have x = 3y - 2.

 

Now solve for y; you get y = (x+2)/3

 

Re-label this as f^-1 = (x+2)/3

 

That's the procedure: interchange x & y, solve for y, re-label it as the inverse of the original function.

 

For the second problem, the inverse will be cube root of x because to solve for the 'new y' you'll have to take the cube root.