Let `f:(-pi/2,pi/2)vecR` be given by `f(x)=(log(sec"x"+tan"x"))^3` then a)`f(x)` is an odd function b)`f(x)` is a one-one function c)`f(x)` is an onto function d)`f(x)` is an even function

Let f:(-pi/2,pi/2)-> RR be given by f(x) = (log(sec x + tan x))^3 Then which of the following is wrong?

If f(x) be an even function. Then f'(x)

Statement 1: If f(x) is an odd function, then f^(prime)(x) is an even function. Statement 2: If f^(prime)(x) is an even function, then f(x) is an odd function.

Let f(x)=e^(e^(|x|sgnx))a n dg(x)=e^(e^(|x|sgnx)),x in R , where { } and [ ] denote the fractional and integral part functions, respectively. Also, h(x)=log(f(x))+log(g(x))dot Then for real x , h(x) is (a)an odd function (b)an even function (c)neither an odd nor an even function (d)both odd and even function

Let f be the function f(x)=cosx-(1-(x^2)/2)dot Then f(x) is an increasing function in (0,oo) f(x) is a decreasing function in (-oo,oo) f(x) is an increasing function in (-oo,oo) f(x) is a decreasing function in (-oo,0)

If f(x) is an odd function then int_(-a)^(a)f(x)dx is …………. .

Let f be a differential function such that f(x)=f(2-x) and g(x)=f(1 +x) then (1) g(x) is an odd function (2) g(x) is an even function (3) graph of f(x) is symmetrical about the line x= 1 (4) f'(1)=0

The function f(x)=sin(log(x+sqrt(1+x^2))) is (a) even function (b) odd function (c) neither even nor odd (d) periodic function

Show that the function f:N to N defined by f(x)=2x-1 is one-one but not onto.