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# Inverses

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the inverse of function $f(x) = \dfrac{2x-1}{x+5}$ is written in the form of $f^{-1}(x)=\dfrac{ax+b}{cx+d}$, where a, b, c, and d are all real numbers. If you could, try to find $\dfrac{a}{c}.$

Apr 15, 2021
edited by SparklingWater2  Apr 15, 2021

#1
+180
+1

https://web2.0calc.com/questions/help-asapp_1

Check this link and let me know if it's wrong.

Hope this helps!

Apr 15, 2021
#2
+507
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It's wrong :P

Apr 15, 2021
#3
+180
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Ok, thank you for telling me. I will solve it immediately.

Mathdory  Apr 15, 2021
#4
+32402
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Replace x by y and f(x) by x in the function definition, then rearrange to  find y:

$$x = \frac{2y-1}{y+5}$$   so  $$x(y+5)=2y-1$$

Collect the y's   $$y(x-2)+5x = -1$$  or $$y = \frac{-5x-1}{x-2}$$

which means $$f^{-1}(x)=\frac{-5x-1}{x-2}$$

So a /c= -5/1

Apr 15, 2021
edited by Alan  Apr 15, 2021