Let us consider two functions f and g, defined by f(x) = 4 – (x – 2)2and g(x) = 6 – x. What is one possible value of a such that f(a) = g(a)?

Question

can someone help me solve this

Answer 1

f(a)=4-(a-2)², g(a)=6-a, so 4-(a-2)²=6-a. This can be written (2-a+2)(2+a-2)=6-a, that is, (4-a)a=6-a.

So 4a-a²=6-a, a²-5a+6=0=(a-3)(a-2). So a=3 or 2 (take your pick!).