How do you find the inverse function $f(x) = -3 x^7-2$ ?

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Answer 1 · 2015-07-18T09:16:53

Let $y=f(x)$ and apply a sequence of operations to both sides of the equation to isolate $x$ and find:

$f^(-1)(y) = -root(7)((y+2)/3)$

Let $y = f(x) = -3x^7-2$

Add $2$ to both ends to get:

$y+2 = -3x^7$

Divide both sides by $-3$ to get:

$x^7 = -(y+2)/3$

Take $7$ th root to get:

$x = root(7)(-(y+2)/3) = -root(7)((y+2)/3)$ (since $(-1)^7 = -1$ )

So $f^(-1)(y) = -root(7)((y+2)/3)$

How do you find the inverse function f(x) = -3 x^7-2f(x) = -3 x^7-2?