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CBSE CLASS XII

Functions and Relations (4/6 Mark)

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1. Consider f : R → [ -5, ∞ ) given by f(x) = 9x²+ 6x-5. Show that f is invertible with .
2. Prove that:
3. Consider defined by f(1) = a, f(2) = b, f(3) = c, g(a) = apple, g(b) = ball ,g(c) = cat. Show that f, g and gof are invertible. Find out f^-1 , g^-1 and (gof)^-1 and show that (gof)^-1 = f^-1o g^-1.
4. Let A = N x N and * be the binary operation on A defined by (a,b)*(c,d) = (a + c, b+d). Show that * is commutative and associative. Find the identity element for * on A, if any.
5. Find the value of x if
6. Let f: N→R be a function defined as f(x) = 4x² + 12 x + 15, where S is the range of f. Show that f: N → S is invertible. Find f^-1.
7. Prove that
8. Prove: 2 tan^-1(1/2) + tan^-1(1/7) = tan^-1(31/17)
9. Solve for x: tan^-12x + tan-13x = π/4
10. Prove that the function f: R →R defined as f(x) = 2x-3 is invertible and find f^-1(x)
11. Show that sin^-1 12 /13 + cos^-1 4/5 + tan^-1 63/16 = π .
12. Show that the relation are in the set a = {x : x є w, x ≤10}given by is an equivalence relation , find the elements related to 3.
13. Examine if the following are binary operations
    (i) a*b =a+b/2,a,b є N
    (ii) a*b=a+b/2, a,b є Q .
14. Let be a function defined as , find f^-1 : Range of .
15. Prove that .
16. Prove: 2 tan^-11/2) + tan^-1(1/7) = tan^-1(31/17).
17. Solve for x: tan^-12x + tan^-13x = π/4.
18. Solve for x : 2 tan^-1( cos x ) = tan^-1 ( 2 cosec x ).
19. Find the value of .
20. Find the value of

 

Submitted By Mrs. E.Praveen
Email Id : [email protected]