Function Of Function

Algebra Level pending

The function $f : \mathbb {R \to R}$ is such that $f(x) = \dfrac x {x^2 +1}$ . Find $f(f(2))$ .

\frac{29}{10}

\frac{1}{29}

29

\frac{10}{29}

2 solutions

Aditya Narayan Sharma
Sep 8, 2016

Put $\displaystyle x=\tan y$ So $\displaystyle f(\tan y) = \frac{\sin 2y}{2}$ which yields $\displaystyle f(f(\tan y)) = \frac{2\sin 2y}{\sin^2 2y+4}$ . We know that $\tan y=2$ & $\sin 2y =\frac{4}{5}$ which makes $\displaystyle f(f(2)) = \frac{40}{116}=\frac{10}{29}$

you're answer is good about calculus but let me tell this is an alzebra so you try by that basic way to solve it as it wanted.

A Former Brilliant Member - 4 years, 9 months ago

this is not calculus. where you find this to be calculus?

Aditya Narayan Sharma - 4 years, 9 months ago

sorry ,thanks for informing mistake

A Former Brilliant Member - 4 years, 9 months ago

A Former Brilliant Member
Sep 7, 2016

Solve for $f(2),$

$f(2)$ gives the value after putting the $x= 2$ is $2/5$

$f(2)=2/5$

then to find $f(f(2))$

put the value $f(2)$ in given equation

$f(f(2))$ gives as

$f(f(2))=(2/5)/(2/5)²+1=10/29$

Function Of Function

2 solutions

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