KCET2024MathematicsFunctions

Let (g f)(x)= x and f g(x)=( x )^2 Then,

Options

Af(x)= ^2 x, g(x)=x
Bf(x)= x , g(x)= x
Cf(x)= ^2 x, g(x)= x
Df(x)= x , g(x)=x^2

Correct answer

C. f(x)= ^2 x, g(x)= x

Step-by-step solution

g(f(x))= x and f(g(x))=( x )^2 (a) f(x)= ^2 x and g(x)=x Now, f(g(x))=f(x)= ^2 x and g(f(x))=g ( ^2 x )= ^2 x (b) f(x)= x and g(x)= x Now, f(g(x))=f( x )= x = (x)^4 and a(f(x))=a( x )= x (c) f(x)= ^2 x and g(x)= x Now, f(g(x))=f( x )= ^2 x and g(f(x))=g ( ^2 x )= ^2 x =| x| (d) f(x)= x and g(x)=x^2 Now, f(g(x))=f (x^2 )= |x| and g(f(x))=g( x )=( x )^2= ^2 x

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