Understanding Inequalities: Solving f(x) < 0 Math Expression and Graph Interpretation

f(x)<0

The expression “f(x)<0" represents a mathematical inequality

The expression “f(x)<0" represents a mathematical inequality. This inequality states that the function f(x) is less than zero. In terms of graphing, this inequality represents the portion of the graph of f(x) that lies below the x-axis. The points on the graph of f(x) are negative. To solve this inequality algebraically, you would follow these steps: 1. Identify the function f(x) whose values you want to analyze. 2. Set up the inequality: f(x) < 0. 3. Determine the intervals where the function is less than zero by finding the x-values that satisfy the inequality. 4. Write the solution as an interval or a union of intervals. For example, let's say we have the function f(x) = x² - 4x + 3. To find the values of x for which f(x) < 0, we can follow these steps: 1. Identify the function: f(x) = x² - 4x + 3. 2. Set up the inequality: x² - 4x + 3 < 0. 3. Solve for x by factoring or using the quadratic formula. In this case, the equation factors as (x - 3)(x - 1) < 0. 4. Find the critical points where the inequality changes. In this case, x = 3 and x = 1. 5. Create a number line and test intervals between these critical points and beyond to determine when the inequality is satisfied. - Test x < 1: Choose a value less than 1, like x = 0. Plugging it into the inequality gives (0 - 3)(0 - 1) < 0, which is true. - Test 1 < x < 3: Choose a value between 1 and 3, like x = 2. Plugging it into the inequality gives (2 - 3)(2 - 1) < 0, which is false. - Test x > 3: Choose a value greater than 3, like x = 4. Plugging it into the inequality gives (4 – 3)(4 – 1) < 0, which is true. 6. Determine the intervals where the inequality is satisfied: x < 1 or x > 3.
7. Write the solution as an interval or union of intervals: (-∞, 1) U (3, ∞).

Note: This is just one example. The approach may differ depending on the specific function and inequality involved. Always consider the graph and perform additional checks to ensure accuracy.

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