Chapter 10: Q. 451 (page 1067)

Find the inverse of the function $f (x) = x^{5} - 9$ .

Short Answer

Expert verified

The inverse of the function is $f^{- 1} (x) = \sqrt[5]{x + 9}$ .

Step by step solution

Step 1. Given information.

Consider the given function,

$f (x) = x^{5} - 9$

Replace $f (x)$ with $y$ ,

$y = x^{5} - 9$

Replace $x$ with $y$ and vice-versa,

$x = y^{5} - 9$

Step 2. Solve for y.

Add $9$ on both sides,

role="math" localid="1645025732251" $x + 9 = y^{5} y = \sqrt[5]{x + 9}$

Replace $y$ with role="math" localid="1645025745429" $f^{- 1} (x)$ ,

$f^{- 1} (x) = \sqrt[5]{x + 9}$

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Find the inverse of the function $f (x) = x^{5} - 9$ .

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Solve for y.

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Short Answer

Step by step solution

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Find the inverse of the function $f (x) = x^{5} - 9$ .