IIT JEE 1983 Maths - True or False Q4

Algebra Level 3

True or False?

If f ( x ) = ( a − x n ) 1 / n f(x)=(a-x^n)^{1/n} , where a > 0 a>0 and n n is a positive integer, then f ( f ( x ) ) = x f(f(x))=x .

In case you are preparing for IIT JEE, you may want to try IIT JEE 1983 Mathematics Archives .
False True

Shubhamkar Ayare by Shubhamkar Ayare , 22, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Chew-Seong Cheong
Jan 11, 2017

f ( x ) = ( a − x n ) 1 n ⟹ f [ f ( x ) ] = ( a − [ f ( x ) ] n ) 1 n = ( a − [ ( a − x n ) 1 n ] n ) 1 n = ( a − ( a − x n ) ) 1 n = ( x n ) 1 n = x \begin{aligned} f(x) & = (a-x^n)^\frac 1n \\ \implies f[f(x)] & = \left(a-[f(x)]^n \right)^\frac 1n \\ & = \left(a-\left[(a-x^n)^\frac 1n \right]^n \right)^\frac 1n \\ & = \left(a-(a-x^n) \right)^\frac 1n \\ & = \left(x^n \right)^\frac 1n \\ & = x \end{aligned}

Therefore, the answer is True \boxed{\text{True}} .

4 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...