If f(x) = 2x + 5 and g(x) = ax − 1, and (f + g)(2) = 10, what is the value of a?

Correct answer: 1

Answer: A, a=1. The sum of functions is defined pointwise: (f+g)(x)=f(x)+g(x). First calculate f(2)=2(2)+5=9. Next calculate g(2)=a(2)−1=2a−1. Therefore (f+g)(2)=9+(2a−1)=2a+8. The question states that this equals 10, so 2a+8=10, 2a=2, and a=1. Checking a=1 gives g(2)=1 and f(2)+g(2)=9+1=10. B, 1/2, would give a sum of 9; C, 2, would give 12; D, −1, would give 6. Thus only A satisfies the condition. A common error is to forget that ax becomes 2a when x=2, not just a. Substitute first, simplify second, and solve the resulting linear equation.