A calculus problem by Aman Dubey

Calculus Level pending

if $f(x) ={ x }^{ 3 }+3x+2$ and $g(f(x))=x$ and $h(g(g(x))=x$ for all $x\quad \in \mathbb R$ then find ${ h }^{ ' }(1)$ .

Notation : $\mathbb R$ denotes the set of real numbers .

333 0 666 111

1 solution

Aman Dubey
Jul 22, 2016

we have ${ h }(g(g(x))=x$

put $x = f(x)$

$\Longrightarrow$ ${ h }(g(g(f(x))=f(x)$

$\Longrightarrow$ ${ h }(g(x)=f(x)$ and do it again

$\Longrightarrow$ ${ h }(g(f(x))=f(f(x))$

So we have

$h(x) = f(f(x))$ and now you know.

Exactly :)

Aniket Sanghi - 4 years, 10 months ago

this is 2016 JEE Advanced question.

Aman Dubey - 4 years, 10 months ago

This was q in a test in my FIITJEE phase test !

Aniket Sanghi - 4 years, 10 months ago

@Aniket Sanghi – Hey Same here... I am in FIITJEE Ghaziabad and u?

Aman Dubey - 4 years, 10 months ago

@Aman Dubey – FIITJEE Raipur , yr phase test score?

Aniket Sanghi - 4 years, 10 months ago

@Aniket Sanghi – 204 in Mains And 172 in Advanced. I think maths Paper 1 (Adv.) was tough I attempted just 4 question in it.

Aman Dubey - 4 years, 10 months ago

@Aniket Sanghi – And Yours?

Aman Dubey - 4 years, 10 months ago

@Aman Dubey – 345 in Mains , 293 in advance ( 129 + 164 )

Aniket Sanghi - 4 years, 10 months ago