Mathematics

 

CHAPTER REVIEW EXERCISE

1. Diagram 1 shows the relation between set J and set K.

State

(a) the codomain of the relation,
(b) the type of the relation.

2. Diagram 2 shows the graph of the function y = f(x).

It is given that f(x)= ax + b. Find

(a) the value of a and of b,
(b) the value of m if m is mapped onto itself under the function f,
(c) the value of x if f ^-1(x) = f ²(x).

6. Functions f and g are defined by f : x → 3x − h and g : x → k/x , x # 0 where h and k are constants. It is given that f ^-1(10) = 4 and fg(2) = 16. Find the value of h and of k.

7. Given that f (x) = 3x − 2 and fg(x) x²-1 , find

(i) the function g
(ii) the value of gf(3)

8. Given f (x) = 2x + 2 and y =| f (x) | . Sketch the graph of y =| f (x) | for the domain 0≤ x ≤ 4. Hence state the corresponding range of y.

9. Given that function h is defined as h : x → px +12 . Given that the value of 3 maps onto itself under the function h, find

(a) the value of p
(b) the value of h^-1 h (-2)

10. Given that the functions h(x) = 2x −1and hh(x) = px + q , where p and q are constants, calculate

(a) the value of p and q
(b) the value of m for which h(−1) = 2m

11. Function g and composite function fg are defined by g : x → x + 3 and fg : x → x² + 6x +7.

(a) Sketch the graph of y = |g(x)| for the domain −5≤ x ≤ 3.
(b) Find f(x).

12. Given quadratic function g(x) = 2x² −3x + 2 . find

(a) g(3),
(b) the possible values of x if g(x) = 22

13. Functions f and g are given as f : x → x² and g : x → px + q , where p and q are constants.

(a) Given that f (1) = g(1) and f (3) = g(5) , find the value of p and of q.
(b) By using the values of p and q obtained in (a), find the functions

(i) gg
(ii) g^-1

14. If w(x) = 3x − 6and v(x) = 6x −1, find

(a) wv(x)
(b) the value of x such that wv(−2x) = x .

15. Given f (x) = |3x − 6| . Find the values of x if f(x) = 3.

 

CBSE Mathematics Class XI ( By Mr. Ayaz Khan )
Email Id : [email protected]