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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

ind the inverse of f and check the answer.(b) Find the domain and the range of f and-example-1

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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

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