JEE MATHEMATICS MCQ: LIMITS

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Analyzing +4 | -1

Suppose

x

is real. Define

f(x)

\frac{x}{2}+1

\begin{aligned} & f^{(2)}(x)=f(f(x)) \\ & f^{(3)}(x)=f\left(f^{(2)}(x)\right) \end{aligned}

and in general

f^{n+1}(x)=f\left(f^{(n)}(x)\right)

for

n \geq 1

where

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

Then

\lim \limits_{{n \rightarrow-\infty}} f^{(n)}(x)

is equal to

View answer and explanation

Correct option: B

Option B (2) is correct because the limit of the recursively defined function

f^{(n)}(x)

as n approaches negative infinity converges to 2.

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