Question

ind the inverse of f and check the answer.(b) Find the domain and the range of f and .(c) Graph f, , and yx on the same coordinate axe

Answer 1

In part a we must find the inverse of:

`f(x)=x^2-10,x\ge0`

For this purpose we'll need to make the following replacements:

`\text{We replace }f(x)\text{ with }x\text{ and }x\text{ with }f^(-1)(x)`

With these replacements we get:

`f(x)=x^2-10\rightarrow x=(f^(-1)(x))^2-10`

So we need to solve this equation for f^(-1):

`x=(f^(-1)(x))^2-10`

We add 10 at both sides of the equation:

`\begin{gathered} x=(f^(-1)(x))^2-10 \\ x+10=(f^(-1)(x))^2-10+10 \\ x+10=(f^(-1)(x))^2 \end{gathered}`

Now we apply the square root at both sides:

`\begin{gathered} x+10=(f^(-1)(x))^2 \\ √(x+10)=\sqrt{(f^(-1)(x))^2} \\ f^(-1)(x)=\sqrt[]{x+10} \end{gathered}`

So the answer to part a is:

`f^(-1)(x)=\sqrt[]{x+10}`

In part b we must find the domain and range of both f and f^(-1). The domain is composed of all the possible x values for which the function ha