Final answer:
The x-intercepts of f(x) are (-1 + √5) / 2 and (-1 - √5) / 2. There is no y-intercept for f(x).
Step-by-step explanation:
To find the x-intercept of f(x), we set y = 0 and solve for x. So, x/x²-1+1 = 0 becomes x/(x²-1) = -1. Cross-multiplying gives x = -(x²-1), which simplifies to x² + x - 1 = 0. Using the quadratic formula, x = (-1 ± √5) / 2. Therefore, the x-intercepts of f(x) are (-1 + √5) / 2 and (-1 - √5) / 2.
To find the y-intercept of f(x), we set x = 0 and solve for y. So, f(0) = 0/0²-1+1 = 0/0 = undefined. Therefore, there is no y-intercept for f(x).