Question 55891
Composite Functions

Given {{{f(x)=x^2-3x+4}}} ; {{{g(x)=x+2}}}

Find: 
For this one substitute g(x) into f(x):
(f o g )(x)=f(g(x))=f(x+2)={{{(x+2)^2-3(x+2)+4}}}
={{{(x+2)(x+2)-3(x+2)+4}}}
={{{(x^2+2x+2x+4)-3x-6+4}}}
={{{x^2+4x+4-3x-6+4}}}
={{{highlight((fog)(x)=x^2+x+2)}}}
:
For this one substitute 2 into f(x) and f(2) into g(x):
(g o f )(2)=g(f(2))={{{g((2)^2-3(2)+4)}}}={{{g(4-6+4)}}}=g(2)
{{{g(2)=(2)+2}}}
{{{highlight((gof)(2)=4)}}}
Happy Calculating!!!