aares1

Hi, I'm having trouble understanding how to solve this. It's from Chung's SAT Math Book.

Let the function f be defined by f(x) = (g(x))^2 - 2g(x) -2. If f(2)=-3, what is the value of g(2)?

Thank you so much

RandomHSer

Just plug in x=2 for the equation,
giving f(2)=-3=g(2)^2-2g(2)-2
adding 3 to both sides gives g(2)^2-2g(2)+1=0
factoring: (g(2)-1)^2=0, g(2)=1

rspence

Yeah, the only way to solve it is simply plug in x = 2. Because you know nothing about g(x).

f(2) = g(2)^2 - 2g(2) - 2, use RandomHSer's solution.