find a symbolic representation

Question

f^-1(x) given f(x)=x^3-2

Answer 1

To find the inverse of a function, all you have to do is switch the variables and solve for y:

f-1(x) represents the inverse of a function.

To find the inverse of f(x), first rewrite the function as : y = x³ - 2

Switch the variables, and our function becomes: x = y³ - 2

Now solve for y: 

1. y³ = x + 2
2. ³√y³= ³√x+2
3. y= ³√x+2

The inverse should look like this:

Note how the domain and range of f(x) are switched.

Hope this helps!