Home
Class 12
MATHS
If RR is the set of real numbers, then f...

If `RR` is the set of real numbers, then functions `f : RR to RR`and `g : RR to RR` are defined respectively by
f(x)`=cos^(2)x+cos^(2)((2pi)/(3)+x)+cos^(2)((2pi)/(3)-x)` and g(x)=2 for all x in `RR`. Show that `(g o f) : RR to RR` is a constantfunction.

Promotional Banner

Similar Questions

Explore conceptually related problems

Let RR be the set of real numbers and the functions f: RR to RR and g : RR to RR be defined by f(x ) = x^(2)+2x-3 and g(x ) = x+1 , then the value of x for which f(g(x)) = g(f(x)) is -

Let RR be the set of real numbers . If the functions f:RR rarr RR and g: RR rarr RR be defined by , f(x)=3x+2 and g(x) =x^(2)+1 , then find ( g o f) and (f o g) .

let the functions f: RR rarr RR and g: RR rarr RR be defined by f(x)=3x+5 and g(x)=x^(2)-3x+2 . Find (i)(g o f) (x^(2)-1), (ii) (f o g )(x+2)

Let the function f:RR rarr RR and g: RR rarr RR be defined by f(x)=x^(2) and g(x)=x+3, evaluate (f o g) (2) , (ii) (g o f) (3)

If RR is the set of real numbers and f(x)=|x|,g(x)=x , find the product function fg.

Two real functions f:[5,oo) to RR and g:[-5,oo) to RR are defined respectively by f(x)=sqrt(x-5) and g(x)=sqrt(x+5), find the function f+g and f-g.

Let RR be the set of real numbers and f : RR to RR be defined by f(x)=sin x, then the range of f(x) is-

Let RR be the set of real numbers and f:RR to RR be given by, f(x)=log_ex. Does f define a function ?

Let f:RR to RR,g:RR to RR and h:RR to RR be differentiable functions such that f(x)=x^(3)+3x+2,g(f(x))=x and h(g(g(x)))=x for all x in RR . Then,

Let the functions f: RR rarr RR and g: RR rarr RR be defined by f(x)=x+1 and g(x)=x-1 Prove that , (g o f)=(f o g)=I_(RR)