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 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 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 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 functions f: RR rarr RR and g: RR rarr RR be given by f(x)=3x-2 and g(x)=3|x|-x^(2) . Find (i) (g o f) (-1) , (ii) (f o g) (-2) , (iii) (g o f) (3), (iv) ( f o g) (4)

Let f:RR rarr RR and g: RR rarr RR be two mapping defined by f(x)=2x+1 and g(x)=x^(2)-2 , find (g o f) and (f o g).

Let the function f: RR rarr RR and g: RR rarr RR be defined by, f(x) =x^(2)-4x+3 and g(x)=3x-2 . Find formulas which define the composite functions (i) f o f (ii) g o g (iii) f o g and (iv) g o f

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).

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 the function f:RR rarr RR be defined by , f(x)=3x-2 and g(x)=3x-2 (RR being the set of real numbers), then (f o g)(x)=