Math

QuestionFind the domain of H(t)=81t29tH(t)=\frac{81-t^{2}}{9-t}.

Studdy Solution

STEP 1

Assumptions1. The function is H(t)=81t9tH(t)=\frac{81-t^{}}{9-t} . We are looking for the domain of this function, which is the set of all possible values of tt that make the function defined.

STEP 1

Assumptions1. The function is H(t)=81t9tH(t)=\frac{81-t^{}}{9-t} . We are looking for the domain of the function, which is the set of all possible input values (t-values) that will output a real number.

STEP 2

The function is defined for all real numbers except where the denominator equals zero, since division by zero is undefined in mathematics. Therefore, we need to find the value of tt for which the denominator 9t9-t equals zero.
9t=09 - t =0

STEP 2

The function will be undefined when the denominator is equal to zero. So, we need to find the value of tt that makes the denominator zero.
9t=09 - t =0

STEP 3

olve the equation for tt.
t=9t =9

STEP 3

olving the equation 9t=09 - t =0 for tt gives us the value of tt that makes the denominator zero.
t=9t =9

STEP 4

The function is undefined when t=9t =9. Therefore, the domain of the function is all real numbers except t=9t =9.
The domain of the function H(t)H(t) is tR,t9t \in \mathbb{R}, t \neq9.

STEP 4

Therefore, the function H(t)H(t) is defined for all real numbers except t=9t =9.
The domain of the function H(t)H(t) is all real numbers except t=9t =9.

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