WORKSHEET CLASS 12 CHAPTER 1

 

1. If A = {1, 2, 3, 4}, B = {3, 4, 5, 6} and f: A → B is defined by f(x) = x + 2, then find f(2) and f^-1(5).
2. If f: R → R is defined by f(x) = x^2 + 2x + 1, find the range of f.
3. If f: R → R is defined by f(x) = |x - 1| + |x - 2| + |x - 3|, find the minimum value of f(x).
4. If f: R → R is defined by f(x) = 3x - 4 and g: R → R is defined by g(x) = x^2, find fog(x) and gof(x).
5. If f: R → R is defined by f(x) = x^2 - 4x + 5, find the value of x for which f(x) = 0.
6. If f: R → R is defined by f(x) = (x + 2)/(x - 3), find the domain and range of f.
7. If f: R → R is defined by f(x) = 2x - 3 and g: R → R is defined by g(x) = 3x + 1, find f(x) + g(x) and f(x)g(x).
8. If f(x) = 3x - 5 and g(x) = x^2 - 4x + 1, find (f o g)(x) and (g o f)(x).
9. Find the domain and range of the function f(x) = (x^2 - 3)/(x - 2).
10. If f(x) = x - 1 and g(x) = 2x + 3, find the composite function (f o g)(x) and (g o f)(x).
11. Find the inverse of the function f(x) = (x - 4)/(x + 3), if it exists.
12. If f(x) = 3x + 1 and g(x) = 2x - 5, find f(g(x)) and g(f(x)).
13. Find the value of k so that the function f(x) = x^2 - 2x + k is strictly increasing.
14. If f(x) = (x^2 + 1)/(x - 1), find the value of f(2) and f(-1).
15. Find the inverse of the function f(x) = (2x + 1)/(x - 1), if it exists.
16. If f(x) = x^2 - 3x + 2 and g(x) = x + 1, find (f o g)(x) and (g o f)(x).
17. Find the domain and range of the function f(x) = (x^2 + 1)/(2x - 3).