Problem 59 - Algebra and Trigonometry Real Mathematics, Real People

Question

Find the domain of the function. $$h(t)=\frac{4}{t}$$

Step-by-Step Solution

Answer

The domain is all real numbers except zero, which is \( t \neq 0 \), or in interval notation, \( (-\infty, 0) \cup (0, \infty) \).

Step 1: Identify where the denominator equals zero

In this function, \( t \) must not be equal to zero to keep the denominator defined. Thus, we should calculate where \( t=0 \). In this function, \( t \) is the only variable in the denominator.

Step 2: Exclude value(s) from the domain

The point where denominator is zero, \( t=0 \), must be excluded from the domain. Thus, all real numbers except zero can be used as input into the function.

Step 3: Declare the Domain

The domain of this function are all real numbers except zero. We can write this as \( t \neq 0 \), or in interval notation as \( (-\infty, 0) \cup (0, \infty) \).