Question 134357
Do you want to find (g o f)(x) (ie g of f of x)?



*[Tex \LARGE (g o f)(x)=g\left(f(x)\right)] Start with the given property


*[Tex \LARGE g\left(f(x)\right)=6(\frac{x-3}{6})+3] Plug in {{{f(x)=(x-3)/6}}} into each x of {{{g(x)=6x+3}}}




{{{g(f(x))=cross(6)((x-3)/cross(6))+3)}}} Multiply. Notice how the 6's cancel



{{{g(f(x))=x-3+3)}}} Simplify



{{{g(f(x))=x+cross(-3+3)}}} Combine like terms. Notice the 3's cancel



{{{g(f(x))=x}}} Simplify