Let `g: Rrarr(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.

Let f(x)=sin^(-1)((2x)/(1+x^(2))) and g(x)=cos^(-1)((x^(2)-1)/(x^(2)+1)) . Then tha value of f(10)-g(100) is equal to

Find the values of k for which |(x^2+k x+1)/(x^2+x+1)|<2,AAx in R

Let f:R->[1,oo) be defined as f(x)=log_10(sqrt(3x^2-4x+k+1)+10) If f(x) is surjective then k =

If f(x)=3x-2, g(x)=2x+k and if fog=gof, then find the value of k.

Let f:""RrarrR be defined by f(x)""= {(k-2x , if xle-1),( 2x+3, if x gt-1):} . If f has a local minimum at x""=""1 , then a possible value of k is (1) 0 (2) -1/2 (3) -1 (4) 1

Suppose a discrete random variable can only take the values 0, 1, and 2. The probability mass function is defined by f(x)={{:((x^(2)+1)/k",", "for x=0,1,2"), (0, "otherwise"):} Find (i) the value of k (ii) cumculative distribution function (iii) P(X ge 1) .

The function f and g are defined by f(x)=6x+8, g(x)=(x-2)/(3) . Calculate the value of gg(1)/(2)

Let g(x)=int(1+2cosx)/((cosx+2)^2)dxa n dg(0)=0. then the value of 8g(pi/2) is __________

The function 'g' defined by g(x)= sin(sin^(-1)sqrt({x}))+cos(sin^(-1)sqrt({x}))-1 (where {x} denotes the functional part function) is (1) an even function (2) a periodic function (3) an odd function (4) neither even nor odd