Question

Determine the x intercepts of the piecewise function in the image that I sent.

Answer 1

To find the x intercept of the function, we would find g(x) = 0

To do this, we would set each expression in the piecewise function to zero and solve for x. We have

For

x/3 + 2 = 0

let us multiply both sides of the equation by 3. We have

x/3 * 3 + 2 * 3 = 0 * 3

x + 6 = 0

x = - 6

- 6 is less than - 1

- 6 < - 1

It satisfies the inequality. Thus, x = - 6 is in the domain

For

4x - 2 = 0

adding 2 to both sides of the equation, we have

4x - 2 + 2 = 0 + 2

4x = 2

Dividing both sides of the equation by 4, we have

4x/4 = 2/4

x = 1/2

x = 1/2 is less than 1. It is not in the domain of this equation. Thus, there is no x interscept at x = 1/2

Therefore, the x intercept of the piecewise function is (- 6, 0)