Question

Let if f and g be functions such that fx=ax²+bx+c and gx=ax b. if g1=2b-a 25 and g2=2a-24, then for what value of x does fx=f8, where x≠8?

Option 1: x = 2
Option 2: x = 4
Option 3: x = -4
Option 4: x = -2

Answer 1

To find the value of x that satisfies the equation f(x) = f(8), we need to substitute the values of f(x) and f(8) into the equation and solve for x using the given values of g1 and g2.

Step-by-step explanation:

To find the value of x that satisfies the equation f(x)=f(8), we first need to determine the values of f(x) and f(8). Given that f(x) = ax²+bx+c and f(8) = a(8)²+b(8)+c, we can substitute these expressions into the equation.

After substituting, we obtain ax²+bx+c = a(8)²+b(8)+c. Since we know that f(x) = ax²+bx+c, we can simplify the equation to ax²+bx+c = a(64)+b(8)+c.

Now, we can subtract ax²+bx+c from both sides of the equation, resulting in 0 = a(64)+b(8). Finally, we can solve for x by referring to the given values of g1 and g2. If we substitute g1 = 2b-a = 25 and g2 = 2a-24 into the equation, we can solve for a and b. Then, we can substitute these values back into the equation to find the value of x.