Question

What is the value of "m" that makes the equation 2f (4) = g(4) true for the functions f(x) = x^2 - 2x + m and and (g(x) = x^2 - 2x + 4m?

A) 1
B) 2
C) 3
D) 4

Answer 1

The value of "m" that makes the equation 2f(4) = g(4) true for the given functions is -2.

Step-by-step explanation:

To find the value of "m" that makes the equation 2f(4) = g(4) true for the functions f(x) = x^2 - 2x + m and g(x) = x^2 - 2x + 4m, we need to substitute the given values into the equations. First, we substitute x = 4 into f(x) and g(x) to get f(4) = (4)^2 - 2(4) + m = 16 - 8 + m = 8 + m, and g(4) = (4)^2 - 2(4) + 4m = 16 - 8 + 4m = 8 + 4m. We can then set up the equation 2(8 + m) = 8 + 4m. Solving this equation will give us the value of "m".

Expanding the equation, we get 16 + 2m = 8 + 4m. Subtracting 16 from both sides, we have 2m = 4 + 4m. Subtracting 4m from both sides, we get -2m = 4. Dividing both sides by -2, we find that m = -2.

Therefore, the value of "m" that makes the equation 2f(4) = g(4) true is -2.