What are the x-intercepts?: g(x) = (4x - 1) (x + 2)

Answer 1

To find the x-intercepts of the function \( g(x) = (4x - 1)(x + 2) \), we need to set \( g(x) = 0 \) and solve for \( x \).

So we set:

\[ (4x - 1)(x + 2) = 0 \]

This equation will be true if either factor equals zero:

1. \( 4x - 1 = 0 \)
2. \( x + 2 = 0 \)

Now, solve each equation:

1. For \( 4x - 1 = 0 \): \[ 4x = 1 \implies x = \frac{1}{4} \]

2. For \( x + 2 = 0 \): \[ x = -2 \]

Thus, the x-intercepts of the function \( g(x) \) are:

\[ \left( \frac{1}{4}, 0 \right) \quad \text{and} \quad (-2, 0) \]

The x-intercepts are \( x = \frac{1}{4} \) and \( x = -2 \).