JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1

Let

f(x)=\frac{x}{\sqrt{1+x^2}}

, then

\underbrace{f o f o f o \ldots \ldots o f}_{n \text { times }}(x)

is:

View answer and explanation

Correct option: B

\frac{x}{\sqrt{1+\left(\sum\limits_{{r=1}}^n 1\right) x^2}}

Option B is correct. By repeatedly applying the function

f(x)=\frac{x}{\sqrt{1+x^2}}

, we observe a pattern that leads to

\underbrace{f o f o f o \ldots \ldots o f}_{n \text { times }}(x) = \frac{x}{\sqrt{1+\left(\sum\limits_{{r=1}}^n 1\right) x^2}}

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