We have a function:
[tex]f(x)=x^2+2x+4[/tex]We have to evaluate f(x+5).
To do so, we replace the argument x from the definition of f(x) with "x+5":
[tex]f(x+5)=(x+5)^2+2(x+5)+4[/tex]Now, we can expand this and simplify as:
[tex]\begin{gathered} f(x+5)=(x+5)^2+2(x+5)+4 \\ f(x+5)=(x^2+2\cdot5x+5^2)+(2x+10)+4 \\ f(x+5)=x^2+10x+25+2x+10+4 \\ f(x+5)=x^2+12x+39 \end{gathered}[/tex]Answer: f(x+5) = x² + 12x +39
