Question

If f(x)=2x^2−3x+1 and g(x)=x+5, what is f(g(x))?

Answer 1

If $f(x)=2x^{2}-3x+1,$ then

$f(g(x))=2[g(x)]^{2}-3g(x)+1\\ \\ f(g(x))=2(x+5)^{2}-3(x+5)+1\\ \\ f(g(x))=2(x^{2}+10x+25)-3(x+5)+1\\ \\ f(g(x))=2x^{2}+20x+50-3x-15+1\\ \\ f(g(x))=2x^{2}+20x-3x+50-15+1\\ \\ \boxed{\begin{array}{c}f(g(x))=2x^{2}+17x+36 \end{array}}$