Which of the following in incorrect ? (A) for any arbitrary integer `1,f(1)=f(-1-1)`

Let f(x) be a differentiable function with f(1)f(-1)!=0. Define a function g(x)=(x^2-1)/(f(x)) . If g(x) does not follow Rolles theorem in [-1,1], then which of the following options is/are FALSE? (a) f(x)=0 cannot have any root in [-1,1] . (b) f(x)=0 has at least one root in [-1,1] . (c) f(x) is zero at at least one point in [-1,1] . (d) f(x) cannot satisfy Rolles theorem in [-1,1] .

If f(x)={[-3x+2,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

f(x)=2x^(3)-3x^(2)-x+(3)/(2) then which of the following is/are incorrect? int_((1)/(3))^((1)/(8))f(f(x))dx=(3)/(4)

Which of the following satisfies the condition f^-1nef . f:R-{-1}toR-{1},f(x)=frac(x)(x+1)

If f:R rarr[-1,1], where f(x)=(sin pi)/(2)[x] where [1 denotes the greatest integer function) then which of the following is false (a) f(x) is onto (b) f(x) is into c) f(x) is periodic (d )f(x) is many one

Let f(x)=(x-1)/(x^(2)), then which of the following is incorrect?

Let f(x)=x^(2)+ax+b be a quadratic polynomial in which a and b are integers. If for a given integer n, f(n) f(n+1)=f(m) for some integer m, then the value of m is

The thylakoid membrane bears several F_0-F_1 particle ATPase/ATP synthase. Which of following is incorrect for these particles?

For any positive integer n , define f_n :(0,oo)rarrR as f_n(x)=sum_(j=1)^ntan^(-1)(1/(1+(x+j)(x+j-1))) for all x in (0, oo) . Here, the inverse trigonometric function tan^(-1)x assumes values in (-pi/2,pi/2)dot Then, which of the following statement(s) is (are) TRUE? sum_(j=1)^5tan^2(f_j(0))=55 (b) sum_(j=1)^(10)(1+fj '(0))sec^2(f_j(0))=10 (c) For any fixed positive integer n , (lim)_(xrarroo)tan(f_n(x))=1/n (d) For any fixed positive integer n , (lim)_(xrarroo)sec^2(f_n(x))=1