⇒If , fog(x)=I(Identity),
gof(x)=I(Identity),
then then f(x) and g(x) are inverses of each other.
![f(x)=(1)/(x-4)\\\\g(x)=(4x+1)/(x)\\\\fog(x)=f[g(x)]=f[(4x+1)/(x)]\\\\=(1)/((4x+1)/(x)-4)\\\\=(x)/(4x+1-4x)\\\\=x\\\\gof(x)=g[f(x)]\\\\g[(1)/(x-4)]\\\\g[f(x)]=((4 *1)/(x-4)+1)/((1)/(x-4))\\\\g[f(x)]=(4+x-4)/(1)\\\\g[f(x)]=x](https://img.qammunity.org/2020/formulas/mathematics/middle-school/bal4vkgvncfc84mnzsuu5yq4jzl11muiu5.png)
fog(x)=x and gof(x)=x
fog=I and gof=I
It means f(x) and g(x) are inverses of each other.
⇒Domain of f(x)=R-{4}, R=Real Number
as⇒ x-4≠0
⇒x≠4
⇒Domain of g(x)=R-{0},R=Set of Real number
As, x≠0.
⇒Domain of the Composition
fog(x)=gof(x)=x
=Set of all Real Number(R)