If `f(x)={[-3x+2,x<1],[(1)/(2)x^(2)+7,x>=1]}` ,then which of the following is not true (A) `f'(1^(+))=1` (B) `f'(1^(-))=-3` (C) `f'(1^(-))=f'(1^(+))=1` (D) f is not differentiable at x=1

If f(x)={x^(3),x^(2) =1 then f(x) is differentiable at

If f(x)=|(log)_(e)x|, then (a) f'(1^(+))=1 (b) f'(1^(-))=-1( c) f'(1)=1(d)f'(1)=-1

Consider f(x)=(x)/(x-1) , which of the following statements is/are correct? (A) f'(0) = -1 (B) f'(2) = -4 (C) f'(3) = -8 (D) f'(4) = -3

If f(x)=|(log)_(2)x|, then f(1^(+))=1 (b) f(1^(-))=-1f(1)=1( c) f'(1)=-1

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) f(1/3).f(2/3)=1 (C) the value of J equals to 1/2 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

The function f is continuous and has the property f(f(x))=1-x for all x in [0,1] and J=int_0^1 f(x)dx . Then which of the following is/are true? (A) f(1/4)+f(3/4)=1 (B) the value of J equals to 1/2 (C) f(1/3).f(2/3)=1 (D) int_0^(pi/2) (sinxdx)/(sinx+cosx)^3 has the same value as J

If f(x) = (x + 1)/(x-1) , then the value of f{f(3)} is :

Let f(x) be a twice differentiable function for all real values of x and satisfies f(1)=1,f(2)=4,f(3)=9. Then which of the following is definitely true? f'(x)=2AA x in(1,3)f'(x)=f(x)=5 for some x in(2,3)f'(x)=3AA x in(2,3)f'(x)=2 for some x in(1,3)

f(x)=([x]+1)/({x}+1) for f:[0,(5)/(2))rarr((1)/(2),3) where [.] represents the fractional part of x .then which of the following is true ? a) f(x) is injective discontinuous function b) f(x) is surjective non differentiable function c)min(lim_(x)1-f(x),lim_(x)1+f(x))=f(1) (d) max ( x values of point of discontinuity) =f(1)

If the graph of y=f(x) is symmetrical about the lines x=1andx=2, then which of the following is true? (a) f(x+1)=f(x)( b) f(x+3)=f(x)(c)f(x+2)=f(x)(d) None of these