what is x when f(x)=0? -1.8 -1.2 0 5

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31-03-2025

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Finding x When f(x) = 0: A Step-by-Step Guide

This article will guide you through the process of determining the value(s) of 'x' when f(x) = 0, given a set of potential x-values: -1.8, -1.2, 0, and 5. We'll explore different approaches depending on the context of the function f(x). The specific solution depends entirely on what function f(x) represents. Without knowing the definition of f(x), we can only explore possibilities.

Understanding the Problem

The equation f(x) = 0 is asking: "For what value(s) of x does the function f(x) equal zero?" This is essentially finding the roots, zeros, or x-intercepts of the function. Graphically, these are the points where the graph of f(x) crosses the x-axis.

Scenario 1: f(x) is a Table of Values

If f(x) is simply represented by the provided data points (-1.8, ?), (-1.2, ?), (0, ?), (5, ?), where the question marks represent the corresponding f(x) values, we need those y-values to proceed.

Let's assume we have a completed table:

In this case, we can directly identify that f(x) = 0 when x = -1.2 and when x = 5.

Scenario 2: f(x) is a Known Function

If f(x) is a defined function (e.g., f(x) = x² - 6x + 5), we would solve the equation f(x) = 0 algebraically.

• Example: Let's say f(x) = x² - 6x + 5. To find where f(x) = 0, we solve:

  x² - 6x + 5 = 0

  This quadratic equation can be factored as:

  (x - 1)(x - 5) = 0

  Therefore, the solutions are x = 1 and x = 5. In this example, only 5 matches our initial provided list.

Scenario 3: Approximation Techniques

If we don't know the explicit form of f(x), but we suspect it's a continuous function, and we only have the x-values, we could potentially use numerical approximation methods (like the Newton-Raphson method) if additional information (such as the values of f(x) at those points) were provided. However, without more data, this isn't possible.

Conclusion:

Determining the value(s) of x where f(x) = 0 requires knowing the nature of the function f(x). With a table of values, the solution is direct. With a defined function, we solve the equation algebraically. Without sufficient information, we cannot definitively determine the answer. The provided x-values (-1.8, -1.2, 0, 5) are only potential candidates; whether any of them are solutions depends on the complete definition of f(x).