Functions Question 179
Question: If $ f(x)=x^{2}+1 $ , then $ {f^{-1}}(17) $ and $ {f^{-1}}(-3) $ will be
[UPSEAT 2003]
Options:
A) 4, 1
B) 4, 0
C) 3, 2
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
Let $ y=x^{2}+1 $
Þ $ x=\pm \sqrt{y-1} $
Þ $ {f^{-1}}(y)=\pm \sqrt{y-1} $
Þ $ {f^{-1}}(x)=\pm \sqrt{x-1} $
Þ $ {f^{-1}}(17)=\pm \sqrt{17-1}=\pm 4 $ and $ {f^{-1}}(-3)=\pm \sqrt{-3-1}=\pm \sqrt{-4} $ , which is not possible.
BETA
