Let the function g:`(-oo,oo)rarr (-pi //2,pi//2)` be given by g(u) `= 2 tan^(-1) (e^u)-pi/2` Then g is

If the function g:(-oo,oo)rarr(-(pi)/(2),(pi)/(2)) is given by g(u)=2tan^(-1)(e^(u))-(pi)/(2). Then g is

If g(x)=2tan^-1(e^x)-pi/2 is Even /odd

Consider the function f:(-oo,oo)rarr(-oo,oo) defined by f(x)=(x^2-ax+1)/(x^2+ax+1), 0ltalt2 , and let g(x)=int_0^(e^x) (f\'(t)dt)/(1+t^2) . Which of the following is true? (A) g\'(x) is positive on (-oo,0) and negative on (0,oo) (B) g\'(x) is negative on (-oo,0) and positive on (0,oo) (C) g\'(x) changes sign on both (-oo,0) and (0,oo) (D) g\'(x) does not change sign on (-oo,oo)

Consider f:(0,oo)rarr(-(pi)/(2),(pi)/(2)), defined as f(x)=tan^(-1)((log_(e)x)/((log_(e)x)^(2)+1))* The about function can be classified as

f: (0,oo) to (-pi/2,pi/2)" be defined as, "f(x)=tan^(-1) (log_(e)x) . The above function can be classified as :

Consider a function f:[0,(pi)/(2)]rarr R given by f(x)=sin x and g:[0,(pi)/(2)]rarr R given by g(x)=cos x. Show that f and g are one-one but f+g is not one-one.

Let f(0,oo) rarr (-oo,oo) be defined as f(x)=e^(x)+ln x and g=f^(-1) , then find the g'(e) .

Let g:R rarr(0,(pi)/(3)) be defined by g(x)=cos^(-1)((x^(2)-k)/(1+x^(2))). Then find the possible values of k for which g is a surjective function.

f:(-(pi)/(2),(pi)/(2))rarr(-oo,oo) defined by f(x)=tan x is