# Question #f7eed

##### 1 Answer
Jun 19, 2017

The possible values of a are 0 and 1. See below for an explanation!

#### Explanation:

1. Set f(x) equal to 2.

$2 - {x}^{2} + {x}^{3} = 2$

2. Subtract 2 from both sides.

$- {x}^{2} + {x}^{3} = 0$

Commutative property:

${x}^{3} - {x}^{2} = 0$

3. Factor and solve.

${x}^{2} \left(x - 1\right) = 0$

${x}^{2} = 0$
$\sqrt{{x}^{2}} = \pm \sqrt{0}$
$\textcolor{red}{x = 0}$

$x - 1 = 0$
$\textcolor{red}{x = 1}$

Therefore, a could equal 0 or 1.