# If f(x)=x^2+1, how do you find f(x+2)?

Feb 13, 2016

# x^2 + 4x + 5

#### Explanation:

to evaluate f(x+2) ,substitute x = x + 2 in f(x)

hence $f \left(x + 2\right) = {\left(x + 2\right)}^{2} + 1$

now ${\left(x + 2\right)}^{2} = {x}^{2} + 4 x + 4$

$\Rightarrow f \left(x + 2\right) = {x}^{2} + 4 x + 4 + 1 = {x}^{2} + 4 x + 5$