If f: R R, g: R R are defined by f(x)=5 x-3, g(x)=x^2+3 , then g o f⁻¹(3) is equal to

Step-by-step solution

Given, f(x)=5 x-3 and g(x)=x^2+3 Let, y=f(x), y=5 x-3y+3=5 x x= y+3 5 f⁻¹(y)= y+3 5 f⁻¹(x)= x+3 5 Now, g(x)=x^2+3 So, g f⁻¹(3)=g [f⁻¹(3) ]=g ( 3+3 5 )=g ( 6 5 )= (6)^2 (5)^2 +3= 36 25 +3= 111 25