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

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Answer 1 · 2018-05-13T21:14:53

$f^(-1)(x)=(sqrt((x+6)/4))-5$

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

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

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

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

$sqrt((x+6)/4)=y+5$

$(sqrt((x+6)/4))-5=y$

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