Question 192113
Note: (f o g)(x) means f(g(x)) and (g o f)(x) means g(f(x))



{{{f(x)=5x-2}}} Start with the first function



{{{f(g(x))=5((x+2)/5)-2}}} Plug in {{{g(x)=(x+2)/5}}}



{{{f(g(x))=cross(5)((x+2)/cross(5))-2}}} Cancel out like terms



{{{f(g(x))=x+2-2}}} Simplify



{{{f(g(x))=x}}} Combine like terms.



--------------------------------------------------


{{{g(x)=(x+2)/5}}} Start with the second function



{{{g(f(x))=((5x-2)+2)/5}}} Plug in {{{f(x)=5x-2}}}



{{{g(f(x))=(5x)/5}}} Combine like terms.



{{{g(f(x))=(cross(5)x)/cross(5)}}} Cancel out like terms.



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




Since we've shown that {{{f(g(x))=x}}} and {{{g(f(x))=x}}}, this means that the two functions are inverses of each other.