How do you find the inverse of $f (x) = 4 {(x + 5)}^{2} - 6$ $f(x) = 4(x + 5)^2 - 6$ ?

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Answer 1 · 2018-05-13T21:14:53

$f^{- 1} (x) = (\sqrt{\frac{x + 6}{4}}) - 5$ $f^(-1)(x)=(sqrt((x+6)/4))-5$

Let $y = 4 {(x + 5)}^{2} - 6$ $y=4(x+5)^2-6$ , swap the letters $x and y$ $x and y$ and then rearrange to make $y$ $y$ the subject.

$x = 4 {(y + 5)}^{2} - 6$ $x=4(y+5)^2-6$

$x + 6 = 4 {(y + 5)}^{2}$ $x+6=4(y+5)^2$

$\frac{x + 6}{4} = {(y + 5)}^{2}$ $(x+6)/4=(y+5)^2$

$\sqrt{\frac{x + 6}{4}} = y + 5$ $sqrt((x+6)/4)=y+5$

$(\sqrt{\frac{x + 6}{4}}) - 5 = y$ $(sqrt((x+6)/4))-5=y$

How do you find the inverse of f(x) = 4(x + 5)^2 - 6f(x)=4(x+5)2−6f(x) = 4(x + 5)^2 - 6?