0
-1
1
∞
2 log e a
1/2 log e a
a loge 2
None of these
A function f : X → X is called an identity function if :
f ( x ) = c , where C is some constant
f (x ) = x
f ( x ) = 1
f ( x ) = x x is rational = 1 - x if x is irrational, then
f is only right continuous at x = 1/2
f is only left continuous at x = 1/2
f is continuous at x = 1/2
f is discontinuous at all points
lim f ( x ) x → a+ = l = ltx → a - g( x ) and Ltx → a - f ( x ) = m = Lt x → a + g ( x ), then the function f ( x ). g ( x )
Is continuous at x = a
Is not continuous at x = a
Has a limit when x → a and it is equal to lm
Has a limit when x → a + bvut it is nto equal to lm
If f ( x ) = x sin 1/x; x ≠ 0 = k; x = 0.is continuous at x = 0, then the value of k is ________.
2
Let f: x → y be a function. Then if R ( f ) y,f is said to be ______.
Into function
Onto function
One - one function
Let f : A →B and A R and B R be defined by y = f (x ), where x A, Y B, then f is called ______.
Real function
One - One function
None
The range of the function is.
( -∞, - 1/4 )
R - { - 1/4, - 1/ 20 }
[ - 1/20, ∞ )
Sin -1 ( cos x ); 0 ≤ x < 1, is equal to
x - π
x - π/2
π/2 -x
π - x
