# Question #e09aa

Apr 28, 2017

Substitute $x + 6$ everywhere there is an x in $f \left(x\right)$ and then simplify.

#### Explanation:

Given:
f(x) = 2x - x^2 + 45

Substitute $x + 6$ for every x:

$f \left(x + 6\right) = 2 \left(x + 6\right) - {\left(x + 6\right)}^{2} + 45$

Simplify:

$f \left(x + 6\right) = 2 x + 12 - \left({x}^{2} + 12 x + 36\right) + 45$

$f \left(x + 6\right) = 2 x + 12 - {x}^{2} - 12 x - 36 + 45$

$f \left(x + 6\right) = - {x}^{2} - 10 x + 21$