Studdy AI Logo
Math  /  Algebra

Question2x2 x \quad 28.) f(x)=1x+3f(x)=\frac{1}{x+3}

Studdy Solution

STEP 1

1. The function given is f(x)=1x+3 f(x) = \frac{1}{x+3} .
2. The function is a rational function, which means it is undefined where the denominator is zero.
3. We need to determine the domain of the function by identifying values of x x that make the denominator zero.

STEP 2

1. Identify the denominator of the function.
2. Determine the values of x x that make the denominator zero.
3. Exclude these values from the domain.
4. State the domain of the function.

STEP 3

Identify the denominator of the function f(x)=1x+3 f(x) = \frac{1}{x+3} .
The denominator is x+3 x + 3 .

STEP 4

Determine the values of x x that make the denominator zero by solving the equation:
x+3=0 x + 3 = 0

STEP 5

Solve the equation x+3=0 x + 3 = 0 for x x :
x=−3 x = -3
This is the value of x x that makes the denominator zero.

STEP 6

Exclude the value x=−3 x = -3 from the domain of the function, as the function is undefined at this point.

STEP 7

State the domain of the function. Since the function is undefined at x=−3 x = -3 , the domain is all real numbers except x=−3 x = -3 .
In interval notation, the domain is:
(−∞,−3)∪(−3,∞) (-\infty, -3) \cup (-3, \infty)
The domain of the function f(x)=1x+3 f(x) = \frac{1}{x+3} is (−∞,−3)∪(−3,∞) \boxed{(-\infty, -3) \cup (-3, \infty)} .

Was this helpful?

Studdy solves anything!

banner

Start learning now

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

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord