Question

Express your answer as a polynomial in standard form. f(x)= f(x)= \,\,3x^2+6x+5 3x 2 +6x+5 g(x)= g(x)= \,\,-x+3 −x+3 \text{Find: }f(g(x)) Find: f(g(x))

Answer 1

Step-by-step explanation:

Given polynomials are

$f(x)=3x^2+6x+5\\g(x)=-x+3$

we need to find out composition of functions f(g(x))  and write it in standard form

To find f(g(x)), we need to replace g(x) with -x+3

$f(g(x))=f(-x+3)$

Now we replace all 'x' in f(x) by -x+3

$f(g(x))=f(-x+3)=3(-x+3)^2+6(-x+3)+5$

Now expand the parenthesis and simplify it

$f(g(x))=3(-x+3)^2+6(-x+3)+5\\f(g(x))=3(x^2-6x+9)+6(-x+3)+5\\f(g(x))=3x^2-18x+27-6x+18+5\\f(g(x))=3x^2-24x+50$