Question

Find a symbolic representation for $f^{-1}(x)$. $$f(x) = \frac{13}{x^3 - 1}$$ $f^{-1}(x)=$ (Simplify your answer. Type an exact answer, using radicals as needed.)

Name: find a symbolic representation for f 1x fx frac13x3 1 f 1x simplify your answer type an exact answer using radicals as needed 47485
Uploaded: 2021-05-28T14:27:36-08:00
Duration: 1 min 6 s
Channel: James Kiss
Description: find a symbolic representation for f 1x fx frac13x3 1 f 1x simplify your answer type an exact answer using radicals as needed 47485

          Find a symbolic representation for $f^{-1}(x)$.
$$f(x) = \frac{13}{x^3 - 1}$$
$f^{-1}(x)=$ (Simplify your answer. Type an exact answer, using radicals as needed.)

$find a symbolic representation for f 1x fx frac13x3 1 f 1x simplify your answer type an exact answer using radicals as needed 47485$

Added by Juan H.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert James Kiss

05/28/2021

Step 1

Then $y = \frac{13}{x^3 - 1}$. To find the inverse function, we need to solve for $x$ in terms of $y$. $$y = \frac{13}{x^3 - 1}$$ $$y(x^3 - 1) = 13$$ $$x^3 - 1 = \frac{13}{y}$$ $$x^3 = \frac{13}{y} + 1$$ $$x^3 = \frac{13 + y}{y}$$ Show more…

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Find a symbolic representation for $f^{-1}(x)$. $$f(x) = \frac{13}{x^3 - 1}$$ $f^{-1}(x)=$ (Simplify your answer. Type an exact answer, using radicals as needed.)