Functions Question 335
Question: If $ f(x)=\frac{x}{\sqrt{1+x^{2}}} $ , then $ (fofof)(x)= $
[RPET 2000]
Options:
A) $ \frac{3x}{\sqrt{1+x^{2}}} $
B) $ \frac{x}{\sqrt{1+3x^{2}}} $
C) $ \frac{3x}{\sqrt{1+x^{2}}} $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ (fofof),(x)=(fof),(f(x))=(fof),( \frac{x}{\sqrt{1+x^{2}}} ) $ $ =f,[ \frac{( \frac{x}{\sqrt{1+x^{2}}} )}{\sqrt{1+\frac{x^{2}}{1+x^{2}}}} ]=f,( \frac{x\sqrt{1+x^{2}}}{\sqrt{1+x^{2}}\sqrt{1+2x^{2}}} ) $ $ =f,( \frac{x}{\sqrt{1+2x^{2}}} )=\frac{\frac{x}{\sqrt{1+2x^{2}}}}{\sqrt{[ 1+\frac{x^{2}}{1+2x^{2}} ]}}=\frac{x}{\sqrt{1+3x^{2}}}. $
BETA
