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Answer 1 · 2017-06-19T21:37:01

The possible values of a are 0 and 1. See below for an 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(x - 1) = 0#

#x^2 = 0#
#sqrt(x^2) = +-sqrt(0)#
#color(red)(x = 0)#

#x-1 = 0#
#color(red)(x=1)#

Therefore, a could equal 0 or 1.