Problems : FUNCTION

Level – I

1. Find the domain of the following functions:

2. Find the range of the following functions:

(i) y = 2 + sinx

3. Find the period of the following, if exists:

(i) f(x) = sinx + {x} where {x} is fractional part of x

(ii) f(x) = tan3x + sin(x/3)

(iii) f(x) = e3lnex-[3x]

Describe the function f + g , f/g and f o g

5. A function is defined for x ≥ 0 as follows:

How is f defined for x ≤ 0 if (i) f is even ? (ii) f is odd ?

Find the even extension of the function .
Is it possible to find the odd extension of the function. Justify your answer .

Define f(f(x)). Also obtain domain and range of f(f(x)).

8. Find the Domain of the function

9. Prove that the function f(x) = cos√x , x ≥ 0 is non-periodic.

10. Find the solution set of the equation