If and and i.e.,

MATHEMATICS · Single correct · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

f(x)=\int \frac{x}{2}\,d\left(\frac{x^2-1}{x^2}\right)

and

f(2)=\frac{1}{2}

and

g_1(x)=f\big(f(f(\dots f(x)\dots))\big)

i.e.,

g_1(x)=f(x)

g_2(x)=f(f(x))

and so on then identify the correct statement(s). (a)

\frac{d}{dx}\big(g_{3n-2}(x)\big)=1

whenever exists,

n\in\mathbb{N}

(b)

\frac{d}{dx}\big(g_{3n}(x)\big)=1

whenever exists,

n\in\mathbb{N}

(c)

\lim_{x\to 1}\frac{\sum_{r=1}^{100}(g_{3r}(x))^r+x-101}{x-1}=5050

(d) Slope of the tangent to the graph of the function

y=g_{80}(x)

x=\frac{1}{2}

4