Question

Find the x-intercepts of the following function and express your result in its lowest form: f(x) = (5x - 1)/(5x^2 + 9x - 2).

Answer 1

The x-intercept of the given function is found by setting the numerator of the rational expression to zero and solving for x, resulting in x = 1/5.

Step-by-step explanation:

To find the x-intercepts of the function f(x) = (5x - 1)/(5x^2 + 9x - 2), one must set the function equal to zero and solve for x. The x-intercept(s) occur where f(x) = 0. In this rational function, the numerator must be zero for the entire function to equal zero (as the denominator cannot be zero), so we set 5x - 1 = 0.

Now we solve for x:

1. Add 1 to both sides: 5x - 1 + 1 = 0 + 1
2. This simplifies to 5x = 1.
3. Now, divide both sides by 5: x = 1/5.

Therefore, the x-intercept is at x = 1/5, which is already in its lowest form.