Problem 56 Find the zero of each function. ... [FREE SOLUTION]

Chapter 15: Problem 56

Find the zero of each function. $$ f(x)=\frac{1}{2} x+2 $$

Short Answer

Expert verified

The zero of the function is x = -4.

Step by step solution

- Understand the Problem

To find the zero of the function, set the function equal to zero and solve for the variable. The zero of a function is the value of x that makes the function equal to zero.

- Write the Equation

Set the given function equal to zero. The function provided is \[ f(x) = \frac{1}{2}x + 2 \]. So, set it equal to zero: \[ \frac{1}{2}x + 2 = 0 \].

- Isolate the Variable

Subtract 2 from both sides to start isolating x: \[ \frac{1}{2}x + 2 - 2 = 0 - 2 \], which simplifies to \[ \frac{1}{2}x = -2 \].

- Solve for x

Multiply both sides by 2 to solve for x: \[ 2 \cdot \frac{1}{2}x = -2 \cdot 2 \], which simplifies to \[ x = -4 \].

- Verify the Solution

Substitute back into the original equation to verify: \[ f(-4) = \frac{1}{2}(-4) + 2 = -2 + 2 = 0 \]. The value x = -4 makes the function equal to zero.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

linear functions

A linear function is one of the simplest types of functions in mathematics. It has the general form of f(x) = mx + b, where m and b are constants. In this type of function, the graph of the equation is a straight line. This makes understanding and working with linear functions straightforward and manageable.

solving equations

Solving equations is a fundamental skill in mathematics. To solve an equation means to find the value of the variable that makes the equation true. For linear functions, this often involves straightforward arithmetic and algebra.

isolation of variables

Isolation of variables is a critical technique in solving equations. It involves manipulating the equation such that the variable of interest stands alone on one side of the equation.

function verification

Function verification is the process of confirming that a potential solution to an equation indeed satisfies the original function. This step ensures accuracy and correctness in mathematical problem-solving.

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91影视

Find the zero of each function. $$ f(x)=\frac{1}{2} x+2 $$

Short Answer

Step by step solution

- Understand the Problem

- Write the Equation

- Isolate the Variable

- Solve for x

- Verify the Solution

Key Concepts

linear functions

solving equations

isolation of variables

function verification

One App. One Place for Learning.

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