How do you find the inverse of $f (x) = 1 - x^{3}$ $f(x) = 1-x^3$ ?

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How do you find the inverse of $f (x) = 1 - x^{3}$ $f(x) = 1-x^3$ ?

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Answer 1 · 2015-11-16T10:59:35

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

Explanation:

$f (x) = 1 - x^{3}$ $f(x)=1-x^3$
One method of finding the inverse of function is by changing the function definition.

Here:
$y = 1 - x^{3}$ $y=1-x^3$

We will now try to write it for x

Adding $x^{3}$ $x^3$ on both sides of equation
$y + x^{3} = 1$ $y+x^3=1$
Subtracting $y$ $y$ from both sides
$x^{3} = 1 - y$ $x^3=1-y$
Taking cube-root on both sides
$x = \sqrt[3]{1 - y}$ $x=root(3)(1-y)$

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

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How do you find the inverse of $f (x) = 1 - x^{3}$ $f(x) = 1-x^3$ ?

1 Answer

Explanation:

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How do you find the inverse of $f (x) = 1 - x^{3}$ $f(x) = 1-x^3$ ?