functions

COMPREHENSION

let f(x) and g(x) are two distinct functions such that f(x) is an odd function and g(x) is an even function for all X ε R . Let a function h(x)=f(x) +g(x) is an odd function and φ(x)=f(g(x))+g(f(x)).

NOW ANSWER THE FOLLOWING QUESTIONS (1-%):

1. Function g(x) is

(a) a trigonometrical function (b) a polynomial function
(c) an absolute function (d) a constant function

2. The number of solutions of f(x)= g(x) is

(a) 1 (b) 2
(c) 0 (d) 3

3. The behaviour of h(x) for all x ε R IS

(a) An increasing function (b)a decreasing function
(c) a constant function (d) nothing can be said

4. The number of solutions of φ(x) = h(x) is
(a) 2 (b) 1
(c) 0 (d) 3

5. For the functions h(x) and φ (x)
(a) h' (x) > φ'(x) (b) h' (x) < φ'(x)
(c) h'(x) ≤ φ'(x) (d) nothing can be said

MULTIPLE CHOICE

7. if f(x) is a polynomial of degree 5 with real coefficients defined for real x such that f(|x|) = 0 has 8 non-zero real roots then f(x) =0 has
(a) 4 positive roots (b) 1 negative root
(c) 5 real roots (d) at least two imaginary roots

11. Let : R→R be defined by f(x) = x² +ax+1/x²+x+1. The set of exhaustive values of a such that f(x) is onto is
(a) (-∞,∞) (b) (-∞,0)
(c) (1,∞) (d) φ