How do you find the inverse of $f (x) = x^{2} - 6 x$ $f(x)=x^2-6x$ ?

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Answer 1 · 2015-10-14T17:25:59

$f^{- 1} (x) = \sqrt{x + 9} + 3$ $f^-1(x)= sqrt(x+9)+3$

First you equate $f (x)$ $f(x)$ to another variable, say $f (x) = y$ $f(x)=y$ .

But before that, complete the square for $f (x)$ $f(x)$ .

$:. x^2-6x+3^2-3^2=(x-3)^2-9$

Now,
$y=(x-3)^2-9$
$(x-3)^2=y+9$
$(x-3)=sqrt(y+9)$
$x=sqrt(y+9)+3$

Now swap back the x for the variable y.

So the inverse for $f(x)$ is
$f^-1(x)= sqrt(x+9)+3$

How do you find the inverse of f(x)=x^2-6xf(x)=x2−6xf(x)=x^2-6x?