Problem 52 Given $f(x)=23 x-1$ and \(g(x)... [FREE SOLUTION]

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Elementary Algebra

John Redden

$Math Studyset 91影视 Explanations$ Math

2011 Edition

Chapter 3: Problem 52

Given $f(x)=23 x-1$ and $g(x)=-3 x+2$ calculate the following. $$ g(-12) $$

Short Answer

Expert verified

The value of $g(-12)$ is 38.

Step by step solution

Identify the Function

We're given the function $g(x) = -3x + 2$ and we're asked to find $g(-12)$. This means we need to substitute $-12$ for $x$ in the function $g(x)$.

Substitute the Value

Substitute $-12$ for $x$ in the function $g(x) = -3x + 2$. This gives us $g(-12) = -3(-12) + 2$.

Perform the Calculation

Calculate $-3(-12) + 2$. Start by multiplying $-3$ and $-12$, which gives $36$. Then, add $2$ to $36$.

Final Answer

Add $36$ and $2$, which results in $38$. Thus, the value of $g(-12)$ is $38$.

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Key Concepts

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

Substitute

When working with functions like $g(x) = -3x + 2$, substitution is a fundamental step that involves replacing the variable with a specific value. In our example, the task was to determine $g(-12)$, meaning we substitute $-12$ for the variable $x$. Here's how you do it:

Identify the function and the value you need to substitute. In this case, the function is $g(x) = -3x + 2$ and the substitution value is $-12$.
Replace $x$ in the expression with $-12$. The function then becomes $g(-12) = -3(-12) + 2$.

Substitution is simply about inserting the given number into the function. It's like filling in the blanks with numbers to make your calculation ready to move on to the next step.

Calculate

After substituting the value into the function, the next step is to perform the calculation. This step involves simplifying the expression you get after substitution. In the example $g(-12) = -3(-12) + 2$, we need to do some arithmetic operations.Here鈥檚 the process:

First, multiply the constants: Calculate $-3\times(-12)$. Multiplying these two negative numbers results in a positive $36$.
Next, add the resulting value to the constant in the equation: Add $36+2$.

These calculations give you a single numerical answer which is the function鈥檚 output for the particular input. Calculation in this context is simply doing basic arithmetic with numbers after substitution.

Evaluate Function

Evaluating a function is essentially finding the output for a given input. In our example, evaluating the function $g(x)$ for $x = -12$ means determining what value the function $g(x) = -3x + 2$ produces when $x$ is $-12$.The steps are:

Substitute the input into the function, which turns $g(x)$ into $g(-12)$.
Calculate the resultant expression, $-3(-12) + 2$, which simplifies to $38$.

Thus, evaluating the function $g$ at $-12$ effectively means calculating its value, yielding $38$, which is the function鈥檚 output. Understanding how to evaluate functions helps in finding specific values that a function can take.

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91影视

Given \(f(x)=23 x-1\) and \(g(x)=-3 x+2\) calculate the following. $$ g(-12) $$

Short Answer

Step by step solution

Identify the Function

Substitute the Value

Perform the Calculation

Final Answer

Key Concepts

Substitute

Calculate

Evaluate Function

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