Question

Consider the functions f (x) = 4/x²and g(x) = 1. (a) solve the inequality f (x) > g(x)

Answer 1

The inequality f(x) > g(x) is true when x ∈ (-2, 0) ∪ (0, 2).

Step-by-step explanation:

We want to solve the inequality f(x) > g(x), which translates to:

4/x^2 > 1

Multiplying both sides by x^2 (note that x cannot be zero), we get:

4 > x^2

Taking the square root of both sides (remembering to consider both positive and negative roots), we have:

-2 < x < 2

However, solutions of x = ±2 need to be excluded as they make the denominator of f(x) zero. Therefore, the final solution is:

x ∈ (-2, 0) ∪ (0, 2)