Class 12 Maths – RD Sharma Chapter 2 : Functions Very Shorts Answer Questions Solutions (Step-by-Step Guide)

RD Sharma Chapter 2 : Functions Very Shorts Answer Questions Solutions

1. Which one of the following graphs represent a function ? Watch Solution
2. Which one of the following graphs represent a one-one function ? Watch Solution
3. If A = {1, 2, 3} and B = {a, b}, write total number of functions from A to B. Watch Solution
4. If A = {a, b, c} and B = {-2, -1, 0, 1, 2}, write total number of one-one functions from A to B. Watch Solution
5. Write total number of one-one functions from set A = {1, 2, 3, 4} to set B = {a, b c}. Watch Solution
6. If f:R→R is defined by f(x)= x^2, write f^-1(25) Watch Solution
7. If f:C→C is defined by f(x) = x^2, write f^-1(-4). Here, C denotes the set of all complex numbers Watch Solution
8. If f:R→R is defined by f(x)= x^3, write f^-1(1) Watch Solution
9. Let C denote the set of all complex numbers. A function f:C→C is defined by f(x) = x^3.Write f^-1(1) Watch Solution
10. Let f be a function from C (set of all complex numbers) to itself given by f(x) =x^3. Write f^-1(-1) Watch Solution
11. If f:R→R is defined by f(x)= x^4, write f^-1(1) Watch Solution
12. If f:C→C is defined by f(x) = x^4, write f^-1(1) Watch Solution
13. If f:R→R is defined by f(x)= x^2, write f^-1(-25) Watch Solution
14. If f : C→C is defined by f(x)= (x – 2)^3, write f^-1(-1) Watch Solution
15. If f : R→R is defined by f(x) = 10x – 7 , then write f^-1(x) Watch Solution
16. If f:(-π/2 , π/2)→R be a function defined by f(x)= cos[x] , then write range(f) Watch Solution
17. If f : R→R is defined by f(x) = 3x- 4 is invertible , then write f^-1(x) Watch Solution
18. If f:R→R, g:R→R are given by f(x) = (x+1)^2 and g(x) = x^2 + 1, then write the value of fog (-3). Watch Solution
19. Let A={x∈R :-4≤x≤4 and x ≠0} and f:A→R is defined by f(x)= ∣x∣/x​ . Write the range of f Watch Solution
20. If f:(-π/2 , π/2)→A be defined by f(x)= sin x. If f is a bijection, write set A Watch Solution
21. Let f:R→R+ be defined by f(x) = a^x, a greater than 0 and a≠ 1. Write f^-1(x) Watch Solution
22. Let f:R-{-1}→R-{1} be given by f(x) = x/ x+1. Write f^-1(x) Watch Solution
23. Let f:R-{-3/5}→R be a function defined as f(x) = 2x/(5x+3) Write f^-1 ; Range of f→ R-{-3/5} Watch Solution
24. Let f:R→R, g:R→R be two functions defined by f(x) = x^2 + x + 1 and g(x) = 1 – x^2. Write fog(-2) Watch Solution
25. Let f:R→R be defined as f(x) = (2x-3)/4. Write fof^-1(1) Watch Solution
26. Let f be an invertible real function. Write (f^-1of)(1) +(f^-1of)(2) +(f^-1of)(3) +…..(f^-1of)(100) Watch Solution
27. Let A = {1, 2, 3, 4} and B = {a, b} be two sets. Write total number of onto functions from A to B Watch Solution
28. Write the domain of the real function f(x) = √x-[x]. Watch Solution
29. Write the domain of the real function f(x) = √[x]-x Watch Solution
30. Write the domain of the real function f(x) = 1/(√[x]-x) Watch Solution
31. Write whether f:R→R given by f(x)= x + √x^2 is one-one, many-one, onto or into. Watch Solution
32. If f(x) = x + 7 and g(x) = x – 7, x ϵ R, write fog(7) Watch Solution
33. What is the range of the function f(x) = |x-1|/(x-1) ? Watch Solution
34. Let f:R→R be defined by f(x) = (3-x^3)^1/3 , then fof(x) Watch Solution
35. If f : R → R is defined by f(x) = 3x + 2, find f(f (x)). Watch Solution
36. Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 6)} be a function from A to B. State whether f is one-one or not. Watch Solution
37. If f : {5, 6} → {2, 3} and g : {2, 3} → {5, 6} are given by f = {(5, 2), (6, 3)} and g = {(2, 5), (3, 6)}, find fog.  Watch Solution
38. Let f : R → R be the function defined by f(x) = 4x – 3 for all x ϵ R. Then write f^-1. Watch Solution
39. Which one the following relations on A = {1, 2, 3} is a function? f = {(1, 3), (2, 3), (3, 2)}, g = {(1, 2), (1, 3), (3, 1)}. Watch Solution
40. Write the domain of the real function f defined by f(x) = √(25-x^2) . Watch Solution
41. Let A= {a, b, c, d} and f :A→A be given by f = {(a,b), (b,d), (c,a), (d,c)}, write f^-1. Watch Solution
42. Let f, g:R → R be defined by f(x)=2x + 1 and g(x)= x^2-2 for all x ϵ R, respectively. Then, find gof Watch Solution
43. If the mapping f:{1, 3, 4}→{1, 2, 5} and g:{1, 2, 5}→{1, 3}, given by f={(1, 2), (3, 5), (4, 1)} and g={(2, 3), (5, 1), (1, 3), write fog. Watch Solution
44. If a function g = {(1, 1), (2, 3), (3, 5), (4, 7)} is described by g(x) = αx + β, find the values of α and β. Watch Solution
45. If f(x) = 4- (x- 7)^3, write f^-1(x) Watch Solution