To determine the inverse of f(x), first replace f(x) with y. Then switch x and y and solve for y.
Inverse: f^(- 1)(x)=sqrt(x-1/5) Is the inverse a function? Yes.
Practice makes perfect
To find the inverse of f(x), we will replace f(x) with y.
f(x)=5x^3+1 → y=5x^3+1
Next step is to switch x and y in the function rule.
y=5 x^3+1 → x=5 y^3+1
Now we need to solve for y. The resulting equation will be the inverse of the given function.
Finally, to indicate that this is the inverse function of f(x), we will replace y with f^(- 1)(x).
y=sqrt(x-1/5) → f^(- 1)(x)=sqrt(x-1/5)
A function is a relation where each input is related to exactly one output. In this case, for each x there is only one value of y. Therefore, f^(- 1)(x) is a function.
