Let the functions `f` and g on the set of real numbers `RR` be defined by, `f(x)= cos x and g(x) =x^(3)`. Prove that, (f o g) `ne` (g o f).

Two functions f and g are defined on the set of real numbers RR by , f(x)= cos x and g(x) =x^(2) , then, (f o g)(x)=

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) .

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)

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 RR be the set of real numbers and f: RR rarr RR be defined by , f(x) =x^(3) +1 , find f^(-1)(x)

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)

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, Rrto RR be defined by f (x)= cos ec x(x ne npi, n in z): then image set of f is-

Let RR be the set of real numbers and f:RR rarr RR be defined by , f(x)=2x +1 . Find g: RR rarr RR , such that (g o f) (x) =10 x+10

Let R be the set of real numbers . If the function f : R to R and g : R to R be defined by f(x) = 4x+1 and g(x)=x^(2)+3, then find (go f ) and (fo g) .