Math / Algebra

QuestionQuestion 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

Studdy Solution

STEP 1

What is this asking? This isn't even a real problem!
It's asking where we should substitute a given value when we want to find a specific input for a function. Watch out! Don't mix up the independent variable ( $x$ ) and the dependent variable ( $f(x)$ )!
If you swap them, you'll end up solving the wrong problem entirely!

STEP 2

1. Understand the relationship
2. Substitute correctly

STEP 3

Remember, the independent variable, usually $x$ , is the input to our function.
It's the thing we control!
The dependent variable, often $f(x)$ or $y$ , is the output – it depends on what we plug in for $x$ .

STEP 4

Think of a vending machine. $x$ is like the button you press (your choice!), and $f(x)$ is the snack that comes out (the result of your choice).

STEP 5

If we know the value of the dependent variable (the snack we want, $f(x)$ ), and we're looking for the independent variable (the button to press, $x$ ), we substitute the given value for $f(x)$ in the equation.

STEP 6

Let's say $f(x) = 2x + 1$ and we want to find $x$ when $f(x) = 7$ .
We substitute $7$ for $f(x)$ in the equation, like this: $7 = 2x + 1$

STEP 7

Now, we just solve for $x$ ! $7 - 1 = 2x$ $6 = 2x$ $\frac{6}{2} = \frac{2x}{2}$ $3 = x$ So, when $f(x)$ is 7, $x$ is 3!

STEP 8

Substitute the given value for the dependent variable, $f(x)$ , into the equation.
Then, solve for the independent variable, $x$ .

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QuestionQuestion 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

Studdy Solution

STEP 1

STEP 2

1. Understand the relationship
2. Substitute correctly

STEP 3

Remember, the independent variable, usually $x$ , is the input to our function.
It's the thing we control!
The dependent variable, often $f(x)$ or $y$ , is the output – it depends on what we plug in for $x$ .

STEP 4

Think of a vending machine. $x$ is like the button you press (your choice!), and $f(x)$ is the snack that comes out (the result of your choice).

STEP 5

If we know the value of the dependent variable (the snack we want, $f(x)$ ), and we're looking for the independent variable (the button to press, $x$ ), we substitute the given value for $f(x)$ in the equation.

STEP 6

Let's say $f(x) = 2x + 1$ and we want to find $x$ when $f(x) = 7$ .
We substitute $7$ for $f(x)$ in the equation, like this: $7 = 2x + 1$

STEP 7

Now, we just solve for $x$ ! $7 - 1 = 2x$ $6 = 2x$ $\frac{6}{2} = \frac{2x}{2}$ $3 = x$ So, when $f(x)$ is 7, $x$ is 3!

STEP 8

Substitute the given value for the dependent variable, $f(x)$ , into the equation.
Then, solve for the independent variable, $x$ .

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QuestionQuestion 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, xxx, for a given value of the dependent variable, f(x)f(x)f(x), then substitute the number in for

Studdy Solution

STEP 1

STEP 2

1. Understand the relationship2. Substitute correctly

STEP 3

Remember, the **independent variable**, usually xxx, is the input to our function.It's the thing *we* control!The **dependent variable**, often f(x)f(x)f(x) or yyy, is the output – it *depends* on what we plug in for xxx.

STEP 4

Think of a vending machine. xxx is like the button you press (your choice!), and f(x)f(x)f(x) is the snack that comes out (the result of your choice).

STEP 5

If we know the value of the **dependent variable** (the snack we want, f(x)f(x)f(x)), and we're looking for the **independent variable** (the button to press, xxx), we substitute the given value for f(x)f(x)f(x) in the equation.

STEP 6

Let's say f(x)=2x+1f(x) = 2x + 1f(x)=2x+1 and we want to find xxx when f(x)=7f(x) = 7f(x)=7.We **substitute** 777 for f(x)f(x)f(x) in the equation, like this: 7=2x+1 7 = 2x + 1 7=2x+1

STEP 7

Now, we just solve for xxx! 7−1=2x 7 - 1 = 2x 7−1=2x 6=2x 6 = 2x 6=2x62=2x2 \frac{6}{2} = \frac{2x}{2} 26​=22x​3=x 3 = x 3=xSo, when f(x)f(x)f(x) is **7**, xxx is **3**!

STEP 8

Substitute the given value for the **dependent variable**, f(x)f(x)f(x), into the equation.Then, solve for the **independent variable**, xxx.

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QuestionQuestion 7 (Mandatory) (1 point) If a problem requires you to determine the value of the independent variable, $x$ , for a given value of the dependent variable, $f(x)$ , then substitute the number in for

1. Understand the relationship
2. Substitute correctly

Remember, the independent variable, usually $x$ , is the input to our function.
It's the thing we control!
The dependent variable, often $f(x)$ or $y$ , is the output – it depends on what we plug in for $x$ .

Think of a vending machine. $x$ is like the button you press (your choice!), and $f(x)$ is the snack that comes out (the result of your choice).

If we know the value of the dependent variable (the snack we want, $f(x)$ ), and we're looking for the independent variable (the button to press, $x$ ), we substitute the given value for $f(x)$ in the equation.

Let's say $f(x) = 2x + 1$ and we want to find $x$ when $f(x) = 7$ .
We substitute $7$ for $f(x)$ in the equation, like this: $7 = 2x + 1$

Now, we just solve for $x$ ! $7 - 1 = 2x$ $6 = 2x$ $\frac{6}{2} = \frac{2x}{2}$ $3 = x$ So, when $f(x)$ is 7, $x$ is 3!

Substitute the given value for the dependent variable, $f(x)$ , into the equation.
Then, solve for the independent variable, $x$ .