Question

Two functions are shown below

f(x)=2x³ +2x-3
g(x)=-0.5|x-4|
what is the y value when f(x) = g(x)?

Answer 1

To find the y value when f(x) equals g(x), set the functions equal and solve for x in both cases considering the absolute value in g(x), and then calculate the corresponding y-values.

Step-by-step explanation:

To find the y value when f(x) = g(x), we need to set the two functions equal to each other and solve for x. This will give us the point(s) of intersection for the functions, if they exist. The functions provided are f(x) = 2x³ + 2x - 3 and g(x) = -0.5| x - 4 |.

We will solve the equation in two cases, since g(x) is defined using the absolute value:

• For x ≥ 4:

2x³ + 2x - 3 = -0.5(x - 4)

• For x < 4:

2x³ + 2x - 3 = -0.5(-x + 4)

Solving these equations will give us the x-intercepts of the point(s) where the two functions intersect. We then substitute the solution(s) back into either f(x) or g(x) to find the corresponding y-values.