Question

Given a(x) = x^2 + 2x + 4 - 10 and b(x) = x + 2, determine a(b) in the form a(b) = c + b(b).

a) a(b) = x^2 + 4x + 8
b) a(b) = x^2 + 2x + 12
c) a(b) = x^2 + 4x + 12
d) a(b) = x^2 + 4x - 8

Answer 1

To determine a(b), substitute b(x) in place of x in a(x) and simplify: a(b) = x^2 + 4x + 12.Correct option is b.

Step-by-step explanation:

To determine a(b) given that a(x) = x^2 + 2x + 4 - 10 and b(x) = x + 2, we substitute b(x) in place of x in a(x) and simplify:

a(b) = (b)^2 + 2(b) + 4 - 10

= (x + 2)^2 + 2(x + 2) + 4 - 10

= x^2 + 4x + 4 + 2x + 4 + 4 - 10

= x^2 + 4x + 12

Therefore, the correct answer is a(b) = x^2 + 4x + 12 (option c).