Math / Algebra

Question $g(x) = \begin{cases} 2x+3, & x > 4 \\ -2x+3, & x \le 4 \end{cases}$
What is $g(7)$ if:
13 -13 17 -17

Studdy Solution

STEP 1

What is this asking? We're given a piecewise function $g(x)$ , which means it acts differently depending on the input $x$ , and we need to find what $g(7)$ is! Watch out! Make sure to plug the $x$ value into the correct piece of the function!
It's easy to get mixed up!

STEP 2

1. Determine the relevant piece
2. Evaluate $g(7)$

STEP 3

Alright, so we have this funky function $g(x)$ that changes its outfit depending on the value of $x$ .
When $x$ is greater than 4, $g(x)$ dresses up as $2x + 3$ .
But when $x$ is less than or equal to 4, it prefers the disguise $-2x + 3$ .

STEP 4

We're trying to find $g(7)$ .
So our $x$ value is 7.
Since 7 is definitely greater than 4, we know which piece to use: the $2x + 3$ one!

STEP 5

Now, let's plug in our $x$ value, which is 7, into the correct piece of the function.
Remember, we decided that since $x=7$ is greater than 4, we're using $g(x) = 2x + 3$ .

STEP 6

So, we substitute $x=7$ into the expression: $g(7) = 2 \cdot 7 + 3$

STEP 7

First, we multiply: $2 \cdot 7 = 14$

STEP 8

Then, we add: $14 + 3 = 17$

STEP 9

So, our final result is: $g(7) = 17$

STEP 10

$g(7) = 17$

Was this helpful?

Question $g(x) = \begin{cases} 2x+3, & x > 4 \\ -2x+3, & x \le 4 \end{cases}$
What is $g(7)$ if:
13 -13 17 -17

Studdy Solution

STEP 1

What is this asking? We're given a piecewise function $g(x)$ , which means it acts differently depending on the input $x$ , and we need to find what $g(7)$ is! Watch out! Make sure to plug the $x$ value into the correct piece of the function!
It's easy to get mixed up!

STEP 2

1. Determine the relevant piece
2. Evaluate $g(7)$

STEP 3

Alright, so we have this funky function $g(x)$ that changes its outfit depending on the value of $x$ .
When $x$ is greater than 4, $g(x)$ dresses up as $2x + 3$ .
But when $x$ is less than or equal to 4, it prefers the disguise $-2x + 3$ .

STEP 4

We're trying to find $g(7)$ .
So our $x$ value is 7.
Since 7 is definitely greater than 4, we know which piece to use: the $2x + 3$ one!

STEP 5

Now, let's plug in our $x$ value, which is 7, into the correct piece of the function.
Remember, we decided that since $x=7$ is greater than 4, we're using $g(x) = 2x + 3$ .

STEP 6

So, we substitute $x=7$ into the expression: $g(7) = 2 \cdot 7 + 3$

STEP 7

First, we multiply: $2 \cdot 7 = 14$

STEP 8

Then, we add: $14 + 3 = 17$

STEP 9

So, our final result is: $g(7) = 17$

STEP 10

$g(7) = 17$

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Questiong(x)={2x+3,x>4−2x+3,x≤4g(x) = \begin{cases} 2x+3, & x > 4 \\ -2x+3, & x \le 4 \end{cases}g(x)={2x+3,−2x+3,​x>4x≤4​What is g(7)g(7)g(7) if:13 -13 17 -17

Studdy Solution

STEP 1

What is this asking? We're given a *piecewise function* g(x)g(x)g(x), which means it acts differently depending on the input xxx, and we need to find what g(7)g(7)g(7) is! Watch out! Make sure to plug the xxx value into the *correct* piece of the function!It's easy to get mixed up!

STEP 2

1. Determine the relevant piece2. Evaluate g(7)g(7)g(7)

STEP 3

Alright, so we have this *funky* function g(x)g(x)g(x) that changes its outfit depending on the value of xxx.When xxx is greater than **4**, g(x)g(x)g(x) dresses up as 2x+32x + 32x+3.But when xxx is less than or equal to **4**, it prefers the disguise −2x+3-2x + 3−2x+3.

STEP 4

We're trying to find g(7)g(7)g(7).So our xxx value is **7**.Since **7** is *definitely* greater than **4**, we know which piece to use: the 2x+32x + 32x+3 one!

STEP 5

Now, let's **plug in** our xxx value, which is **7**, into the *correct* piece of the function.Remember, we decided that since x=7x=7x=7 is greater than 4, we're using g(x)=2x+3g(x) = 2x + 3g(x)=2x+3.

STEP 6

So, we **substitute** x=7x=7x=7 into the expression: g(7)=2⋅7+3g(7) = 2 \cdot 7 + 3g(7)=2⋅7+3

STEP 7

First, we **multiply**: 2⋅7=142 \cdot 7 = 142⋅7=14

STEP 8

Then, we **add**: 14+3=1714 + 3 = 1714+3=17

STEP 9

So, our **final result** is: g(7)=17g(7) = 17g(7)=17

STEP 10

g(7)=17g(7) = 17g(7)=17

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Question $g(x) = \begin{cases} 2x+3, & x > 4 \\ -2x+3, & x \le 4 \end{cases}$
What is $g(7)$ if:
13 -13 17 -17

What is this asking? We're given a piecewise function $g(x)$ , which means it acts differently depending on the input $x$ , and we need to find what $g(7)$ is! Watch out! Make sure to plug the $x$ value into the correct piece of the function!
It's easy to get mixed up!

1. Determine the relevant piece
2. Evaluate $g(7)$

Alright, so we have this funky function $g(x)$ that changes its outfit depending on the value of $x$ .
When $x$ is greater than 4, $g(x)$ dresses up as $2x + 3$ .
But when $x$ is less than or equal to 4, it prefers the disguise $-2x + 3$ .

We're trying to find $g(7)$ .
So our $x$ value is 7.
Since 7 is definitely greater than 4, we know which piece to use: the $2x + 3$ one!

Now, let's plug in our $x$ value, which is 7, into the correct piece of the function.
Remember, we decided that since $x=7$ is greater than 4, we're using $g(x) = 2x + 3$ .

So, we substitute $x=7$ into the expression: $g(7) = 2 \cdot 7 + 3$

First, we multiply: $2 \cdot 7 = 14$

Then, we add: $14 + 3 = 17$

So, our final result is: $g(7) = 17$

$g(7) = 17$