How do you find the inverse of $f (x) = 3 + \sqrt{x - 8}$ $f(x)=3+sqrt(x-8)$ ?

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How do you find the inverse of $f (x) = 3 + \sqrt{x - 8}$ $f(x)=3+sqrt(x-8)$ ?

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Answer 1 · 2015-06-05T13:24:20

Answer: The inverse function is $f (x) = x^{2} - 6 x + 17$ $f(x)=x^2-6x+17$

Explanation: We have the equation $y = 3 + \sqrt{x - 8}$ $y=3+sqrt(x-8)$ .

In order to find the inverse function, we have to switch the variables $x$ $x$ and $y$ $y$ and then solve for $y$ $y$ :

$x = 3 + \sqrt{y - 8}$ $x=3+sqrt(y-8)$ $\Rightarrow$ $=>$ $\sqrt{y - 8} = x - 3$ $sqrt(y-8)=x-3$ $\Rightarrow$ $=>$ $y - 8 = {(x - 3)}^{2}$ $y-8 = (x-3)^2$ $\Rightarrow$ $=>$ $y = {(x - 3)}^{2} + 8$ $y= (x-3)^2 +8$ $\Rightarrow$ $=>$ $y = x^{2} - 6 x + 17$ $y=x^2-6x+17$

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How do you find the inverse of $f (x) = 3 + \sqrt{x - 8}$ $f(x)=3+sqrt(x-8)$ ?

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How do you find the inverse of $f (x) = 3 + \sqrt{x - 8}$ $f(x)=3+sqrt(x-8)$ ?