If f: R R, g: R R be two functions given by f(x)=2 x-3 and g(x)=x^3+5 , then (f g)⁻¹(x) is equal to

Step-by-step solution

aligned & f(x)=2 x-3 & g(x)=x^3+5 & fog (x)=f[g(x)]=f (x^3+5 ) & =2 (x^3+5 )-3 & fog (x)=2 x^3+7=y( say ) aligned aligned & 2 x^3=y-7 & x= [ y-7 2 ]^ 1 3 & fog ⁻¹(y)= [ y-7 2 ]^ 1 3 & fog ⁻¹(x)= [ x-7 2 ]^ 1 3 aligned