Question

For the function f(x)=(x+6)^3 find f^-1(x) PLEASE HELP THANK YOU!

Answer 1

Answer: $f^{-1}(x) = -6+\sqrt[3]{x}$

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Explanation:

Replace f(x) with y.

Swap x and y, then solve for y to get the inverse.

$f(x) = (x+6)^3\\\\y = (x+6)^3\\\\x = (y+6)^3\\\\\sqrt[3]{x} = y+6\\\\y = -6+\sqrt[3]{x}\\\\f^{-1}(x) = -6+\sqrt[3]{x}$

To solve for y, I first applied the cube root to both sides. Then I subtracted 6 from both sides.