Which of the following statements are incorrect? If `f(x) and g (x)` are one to one then `f(x) + g(x)` is also one to one

Which of the following statements are incorrect? If f(x) and g(x) are one-one then f(x)+g(x) is also one-one If f(x) and g(x) are one-one then f(x)dotg(x) is also one-one If f(x) is odd then it is necessarily one-one? Ia n dI Ion l y b. I Ia n dI I Ion l y c. I I Ia n dIon l y d. I ,I Ia n dI I I

Which one of the following statement is correct in respect of the function f(x)= x^(3) sin x ?

Which of the following functions are one-one? f:R rarr R defined by f(x)=-|x|

Statement-1 : If f(x) and g(x) are one-one functions then f(g(x)) and g(f(x)) is also a one-one function. and Statement-2 The composite function of two one-one function may or many not be one-one.

Let f(x) = sqrt(2-x-x^(2)) and g(x) = cos x . Which of the following statement are true ? (I) Domain of f((f(x))^(2)) = Domain of f(g(x)) (II) Domain of f(g(x)) + g(f(x)) = Domain of f(g(x)) (III) Domain of f(g(x)) = Domain of f(g(x)) (IV) Domain of g((f(x))^(3)) = Domain of f(g(x))

Which of the following statement(s) is (are) INCORRECT ?. (A) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f(g(x)) also does not exist.(B) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f'(g(x)) also does not exist.(C) If lim_(x->c) f(x) exists and lim_(x->c) g(x) does not exist then lim_(x->c) g(f(x)) does not exist. (D) If lim_(x->c) f(x) and lim_(x->c) g(x) both exist then lim_(x->c) f(g(x)) and lim_(x->c) g(f(x)) also exist.

Let N be the set of natural numbers and f : N->N be a function given by f(x)=x+1 for x in N.Which one of the following is correct? a. f is one-one and onto b. f is one-one but not onto c. f is only onto d. f is neither one-one nor onto

Consider that f : A rarr B (i) If f(x) is one-one f(x_(1)) = f(x_(2)) hArr x_(1) = x_(2) or f'(x) ge 0 or f'(x) le 0 . (ii) If f(x) is onto the range of f(x) = B. (iii) If f(x) and g(x) are inverse of each other then f(g(x)) = g(f(x)) = x. Now consider the answer of the following questions. If f(x) and g(x) are mirror image of each other through y = x and such that f(x) = e^(x) + x then the value of g'(1) is