How do you find the inverse of $f (x) = x^{3} + 5$ $f(x) = x^3 + 5$ and is it a function?

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Answer 1 · 2018-07-28T12:48:51

$f^{- 1} (x) = \sqrt[3]{x - 5}$ $f^-1(x) = root (3) (x-5)$ , yes it is a function.

$f (x) = x^{3} + 5$ $f(x) = x^3+5$ or

$y = x^{3} + 5$ $y = x^3+5$ or

$x = y^{3} + 5$ $x = y^3+5$ [switch $x and y$ $x and y$ and solve for y]

$y^{3} = x - 5 or y = \sqrt[3]{x - 5}$ $y^3= x-5 or y = root (3) (x-5)$ or

$f^{- 1} (x) = \sqrt[3]{x - 5}$ $f^-1(x) = root (3) (x-5)$

Since in the equation one $x$ $x$ yield exactly one $y$ $y$ , then

it is a function.

graph{y=(x-5)^(1/3) [-10, 10, -5, 5]}[Ans]

How do you find the inverse of f(x)=x3+5f(x) = x^3 + 5 and is it a function?