Let `A={x in RR :-1 le xle 1}` and functions f and g from A to A be defined by , `f(x) =x^(2)` and `g(x) =x^(5)` . Show that `g^(-1)` exists but `f^(-1)` does not exist

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 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 A={x in RR:-1 le x le 1} =B . Prove that , the mapping from A to B defined by f(x)= sin pi x is surjective.

Let the function f: RR rarr RR be defined by, f(x) =x^(2), . Find (i) f^(-1) (25) , (ii) f^(-1) (5) , (iii) f^(-1) (-5)

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 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 C be the set of complex numbers and the function f:RR to RR,g:C to C be defined by f(x) =x^2 and g(x)=x^2 state with reason whether f = g or not.

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 R be the set of real numbers and the mappings f:R toR" and "g:RtoR be defined by f(x)=5-x^2" and " g(x)=3x-5 , then the value of (f@g)(-1) is