Question

given the function: f(x)=x^2-2x. how can you restrict the domain so that f(x) has an inverse? what is the equation of the inverse function?

Answer 1

We have the following equation given:

`y=x^2-2x=x(x-2)`

For this case we can do the following:

`x=y^2-2y=y(y-2)`

We can solve for the quadratic equation and we got:

`y=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(1\cdot-x)}}{2\cdot1}=\frac{2\pm\sqrt[]{4\cdot(1+x)}}{2}=1\pm\sqrt[]{1+x}`

The two solutions are:

`y_1=1-\sqrt[]{1+x},y_2=1+\sqrt[]{1+x}`

Then the answer is:

Part 1

`x\ge1`

Part 2

`f^(-1)(x)=1+\sqrt[]{1+x}`