Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11
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If F(X) = (A − Xn)1/N, a > 0 and N ∈ N, Then Prove that F(F(X)) = X for All X. - Mathematics

If f(x) = (a − xn)1/na > 0 and n ∈ N, then prove that f(f(x)) = x for all x.

 
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Solution

Given:
f(x) = (a − xn)1/na > 0
Now,
f(x)} = f (a − xn)1/n
             = [a – {(– xn)1/n}n]1/n
             = [ – (a – xn)]1/n
             = [ a – a + xn)]1/n = (xn)1/n = x(n × 1/n) = x

Thus, f(f(x)) = x.
Hence proved.

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 3 Functions
Exercise 3.2 | Q 10 | Page 12
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