Which of the following function/functions has/have point of inflection? `f(x)=x^(6/7)` (b) `f(x)=x^6` `f(x)=cosx+2x` (d) `f(x)=x|x|`

Which of the following function from Z to itself are bijections? f(x)=x^(3)( b) f(x)=x+2f(x)=2x+1( d )f(x)=x^(2)+x

Which of the following functions is the inverse of itself? f(x)=(1-x)/(1+x) (b) f(x)=5^(log x)f(x)=2^(x(x-1))(d) None of these

In which of the following function,range is not singleton set f(x)=[x]+[-x]( b) f(x)={x}+{-x}f(x)=|sgn(x)|(d)f(x)=[sqrt(x-[x]) where [x],{x}, and sgn(x) are greatest integer function,fractional part function and signum function respectively.

In which of the following cases, the function f(x) has vertical tangent at x = 0 ? f(x)=x^(2//3)

If f(x) is a real valued function, then which of the following is injective function ? (i) f(x) = x^(5) (ii) f(x) = x + sin x (iii) f(x) = x^(2) (iv) f(x) = e^(x) (v) f(x) = x^(3) + x^(2) + 4x + 4

For which of the following functions f(0) exists such that f(x) is continuous at x=0f(x)=(1)/((log_(e)|x|) b.f(x)=(cos((sin|x|)/(x))) c.f(x)=x sin((pi)/(x)) d.f(x)=(1)/(1+2^( cot x))

Which of the following is an even function a )f(x)=(a^(x)+a^(-x))/(a^(x)-a^(-x)) b) f(x)=(a^(x)+1)/(a^(x)-1) c) f(x)=x(a^(x)-1)/(a^(x)+1)(d)f(x)=log_(2)(x+sqrt(x^(2)+1))

Find the intervals in which the following functions are (a)increasing (b)decreasing f(x)=x^2-6x+7

Find the intervals of monotonicity of the following functions. (i) f(x) =-x^(3) +6x^(2)-gx-2 (ii) f(x) =x+(1)/(x+1) (iii) f(x) =x. e^(x-x^(2)) (iv) f(x) =x- cosx

Examine the following functions for continuity. (a) f(x)=x-5 (b) f(x)=1/(x-5) (c) f(x)=(x^2-25)/(x+5) (d) f(x)=|x-5|