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Someone please help with these 2 questions. Q. Find inverse of the following functions (solve for x) i) y = (x^3+5)/(x-3) ii) y = (x^3-8)/(x^2-4)

Someone please help with these 2 questions.

Q. Find inverse of the following functions (solve for x)
i)    y = (x^3+5)/(x-3)
ii)   y = (x^3-8)/(x^2-4)

Grade:

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
6 years ago
Ans:
(ii)
f(x) = \frac{x^{3}-8}{x^{2}-4}
f(f^{-1}(x)) = \frac{(f^{-1}(x))^{3}-8}{(f^{-1}(x))^{2}-4}
(f^{-1}(x))^{3}-x(f^{-1}(x))^{2}+4x-8=0
f^{-1}(x) = \frac{x-2}{2}\pm \frac{1}{2}\sqrt{x^{2}+4x-12}
Inverse of (i) can not be find in terms of standard mathematical functions.
Thanks & Regards
Jitender Singh
IIT Delhi
askIITians Faculty

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