Functions Question 46
Question: If $ f(x)=3x-5 $ , then $ {f^{-1}}(x) $
[IIT 1998]
Options:
A) Is given by $ \frac{1}{3x-5} $
B) Is given by $ \frac{x+5}{3} $
C) Does not exist because f is not one-one
D) Does not exist because f is not onto
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ f(x)=y\Rightarrow x={f^{-1}}(y). $ Hence $ f(x)=y=3x-5\Rightarrow x=\frac{y+5}{3},\Rightarrow ,{f^{-1}}(y)=x=\frac{y+5}{3} $
$ \therefore {f^{-1}}(x)=\frac{x+5}{3} $ Also f is one-one and onto, so $ {f^{-1}} $ exists and is given by $ {f^{-1}}(x)=\frac{x+5}{3} $ .
BETA
