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**Q. 1. If f(x) = (a –x ^{n})^{1/n} where a > 0 and n is a positive integer, then f[f(x)] = x.**

**Ans. **T

**Solution. **f (x) = (a – x^{n})^{1/n}, a > 0, n is + veinteger

f (f (x)) = f [(a – x^{n})^{1/n}] = [a –{(a – x^{n})^{1/n}}n]^{1/n }

= (a – a + xn)1/n = x

**Q. 2. The function ** i**s 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 f _{1}(x) and f_{2}(x) are defined on domains D_{1} and D_{2} respectively, then f_{1} (x) + f_{2} (x) is defined on D_{1} ∪ D_{2}.**

**Ans. **F

**Solution. **We know that sum of any two functions is defined only on the points where both f_{1} as well as f_{2} are defined that is f_{1} + f_{2} is defined on D_{1} ∩ D_{2}.

∴ The given statement is false.

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