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The function f(x) is one-to-one. For X-7 a. Find an equation for f(x), the inverse function b. Verify that your equation is correct by showing a. Select the correct choice below and, if nec Jse integers or fractio



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Solution

We have the following function given:

[tex]f(x)=\frac{x+21}{x-7}[/tex]

For this case we need to interchange x by y and we have:

[tex]x=\frac{y+21}{y-7}[/tex]

And we need to solve for x and we have:

[tex]x(y-7)=y+21[/tex][tex]xy-7x=y+21[/tex][tex]xy-y=7x+21[/tex]

Solving for y we got:

[tex]y(x-1)=7x+21[/tex][tex]y=\frac{7x+21}{x-1}[/tex]

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