The function f : `RR to RR` is defined by f(x) = sin x + cos x is

The function f : RR to RR is defined by f(x) = ((x^(2)+cos x)(1+x^(4)))/((x-sinx )(2x-x^(3)))+e^(-|x|) is

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

Let the function f:RR rarr RR and g:RR be defined by f(x) = sin x and g(x)=x^(2) . Show that, (g o f) ne (f o g) .

Find the image set of the domain of each of the following functions : f:RR to RR defined by, f(x) = cosecx for all x in RR (pi ne n pi , n in ZZ)

If the function f: RR rarr RR be defined by, f(x)={(x " when "x in QQ ),(1-x " when " x in QQ ):} then prove that , (f o f)=I_(RR) .

If the function f:RR to RR is given by f(x) = x for all x inRR and the function g:RR-{0} to RR is given by g(x)=(1/x), "for all "x in RR-{0}, then find the function f+g and f-g.

If the function f: R to R is defined by f(x) =(x^(2)+1)^(35) for all x in RR then f is

Let t the function f:RR to RR be defined by, f(x)=a^x(a gt0 ,a ne1). Find range of f