Let `A ={0,1,2,3} , B ={1,4,7,10 }`,
`C={5,11,17,23} and f: A rarr B , G: B rarr C` be defined by `f(x)=3x+1 and g(x)=2x+3`, verify that,
`(g o f)^(-1)=(f^(-1)) o g^(-1)`

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 the mapping f: A rarr B and g: B rarr C be defined by f(x)=5/x -1 and g(x)=2+x Find the product mapping ( g o f ).

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 A= {-1,-2,0,1(5)/(2), 3}, B={-6,-5,0,1,4,9} and f: A rarr B be defined by f(x)=2x^(2) -3x-5 . Find f(A). Is f(A)=B ?

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 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 f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (g circ f)^(-1)(x)

Let the functions f: QQ rarr QQ and g: QQ rarr QQ be defined by, f(x)=3x and g(x)=x+3 . Assuming that f and g are both invertible , verify that , ( g o f) ^(-1) =(f^(-1) o g ^(-1)) .

Let f:R to R and g:R to R is define by f(x)=2x+3 and g(x)=3x-2 , then find (g circ f)(-1)