Verified answer

f(x) = { x+1 x ≤ a

........{ x^2 x > a

Let's set both of our pieces equal to each other and plug in 'a' for x. Doing so gives:

a + 1 = (a + 1)^2 (I plugged in a + 1 because x^2 is defined for #'s greater than 'a'.)

a + 1 = a^2 + 2a + 1

0 = a^2 + a

0 = a(a + 1)

a = 0 & -1.

Hope this helped and have a pleasant evening.