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Problem Set 39 Inverse Functions 1.) Let $f(x) = 2x - 5$ and $f^{-1}(x) = \frac{x+5}{2}$. Show that $f \circ f^{-1}$ and $f^{-1} \circ f$ are both equal to the identity function, thus verifying that the functions are inverses. 2.) Find $f^{-1}$ for $f(x) = 7x - 13$. 3.) Find $f^{-1}$ for $f(x) = x^3 + 2$. 4.) Find $f^{-1}$ for $f(x) = \frac{x+3}{x-1}$. 5.) Let $f: [2, \infty) \rightarrow [0, \infty)$ such that $f(x) = \sqrt{x-2}$. Find $f^{-1}$.

Name: problem set 39 inverse functions 1 let fx 2x 5 and f 1x fracx52 show that f circ f 1 and f 1 circ f are both equal to the identity function thus verifying that the functions are inverses 2 f 03414
Uploaded: 2021-09-03T15:39:08-08:00
Duration: 2 min 47 s
Channel: Jon Southam
Description: problem set 39 inverse functions 1 let fx 2x 5 and f 1x fracx52 show that f circ f 1 and f 1 circ f are both equal to the identity function thus verifying that the functions are inverses 2 f 03414

          Problem Set 39 Inverse Functions
1.) Let $f(x) = 2x - 5$ and $f^{-1}(x) = \frac{x+5}{2}$. Show that $f \circ f^{-1}$ and $f^{-1} \circ f$ are both equal to the identity function, thus verifying that the functions are inverses.
2.) Find $f^{-1}$ for $f(x) = 7x - 13$.
3.) Find $f^{-1}$ for $f(x) = x^3 + 2$.
4.) Find $f^{-1}$ for $f(x) = \frac{x+3}{x-1}$.
5.) Let $f: [2, \infty) \rightarrow [0, \infty)$ such that $f(x) = \sqrt{x-2}$. Find $f^{-1}$.

$problem set 39 inverse functions 1 let fx 2x 5 and f 1x fracx52 show that f circ f 1 and f 1 circ f are both equal to the identity function thus verifying that the functions are inverses 2 f 03414$

Added by Alvaro H.

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