Relations Question 5
Question: If $ f(x) $ is an invertible function and $ g( x )=2f( x )+5, $ then the value of $ {g^{-1}}(x) $ is
Options:
A) $ 2{f^{-1}}(x)-5 $
B) $ \frac{1}{2{f^{-1}}(x)+5} $
C) $ \frac{1}{2}{f^{-1}}(x)=5 $
D) $ {f^{-1}}( \frac{x-5}{2} ) $
Show Answer
Answer:
Correct Answer: D
Solution:
Replacing $ x $ by $ {g^{-1}}(x) $ , we get $ x=2f({g^{-1}}(x))+5 $
$ \therefore f({g^{-1}}(x))=\frac{x-5}{2} $
$ \therefore {g^{-1}}(x)={f^{-1}}( \frac{x-5}{2} ) $
BETA
