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JEE Advanced (True/False): Functions | Chapter-wise Tests for JEE Main & Advanced PDF Download
Q. 1. If f(x) = (a –xn)1/n where a > 0 and n is a positive integer, then f[f(x)] = x.
Ans. T
Solution. f (x) = (a – xn)1/n, a > 0, n is + veinteger
f (f (x)) = f [(a – xn)1/n] = [a –{(a – xn)1/n}n]1/n
= (a – a + xn)1/n = x
Q. 2. The function 
is not one -to -one.
Ans. T
Solution. KEY CONCEPT : A function is one-one if it is strictly increasing or strictly decreasing, other wise it is many one.
Q. 3. If f1(x) and f2(x) are defined on domains D1 and D2 respectively, then f1 (x) + f2 (x) is defined on D1 ∪ D2.
Ans. F
Solution. We know that sum of any two functions is defined only on the points where both f1 as well as f2 are defined that is f1 + f2 is defined on D1 ∩ D2.
∴ The given statement is false.
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