FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 3.21- (i) A function f(x) is defined as follows :
f(x) = x + 1, when x ≤ 1.
= 3 – ax^2 when x > 1.
For what value of a will f(x) be continuous? With this value of a draw the graph of f(x). [Ans.1]
(ii) Show that f x( )=x 2^1 − is discontinuous at x = 2.- Show that f(x) is continuous at x = 0 and x = 1, where
f(x) = x^2 , x ≤ 0
= x, 0 < x < 1
= 2 – x, x ≥ 1. - A function f(x) is defined as follows :
f(x) = 1, x > 0
= 0, x = 0
= – 1, x < 0
Show that it is discontinuous at x = 0.
OBJECTIVE QUESTIONS :
- If f(x) = (x – 1) (x – 2) (x – 3), find f(0)
[Ans. – 6] - If f(x) = x + | x |, find f(– 2) [Ans. 0]
- If ( )
2
2
f x x 6x 8
x 8x 12= − +
+ + find f(0) [Ans.2
3
2
3 ]
- Given f(x) = x, ( )
x^2
F x =x, is F(x) = f(x) always? [Ans. equal for x ≠ 0] - If f(x)= 2 + x, x < 3 [Ans. 4]
= 7 – x, x ≥ 3, find f(3) - If f(x)= (x – 2) (x – 3) (x + 4) find f(3) [Ans. 0]
- Given f x x,( )= for what value of x, f(x) is undefined? [Ans. – 1]
- Find the range of the function f x( )=x 22 x−− , x 2≠ [Ans. – 1]
- If f(x) = x + 2x^3 , find – f(– x) [Ans. x + 2x^3 ]
- ( )
f x x, x 0
= x ≠ and is a real number, find f c f c .( )− (− ) [Ans. 2] - If f(x) = e3x + 4, find f(1) + f(2) + f(5) [Ans. e^36 ]