Problem 13
Question
Find the domain of each function. $$h(x)=\frac{4}{\frac{3}{x}-1}$$
Step-by-Step Solution
Verified Answer
The domain of the function h(x) is all real numbers except 3.
1Step 1: Identify the denominator
In h(x), the denominator is \(\frac{3}{x}-1\). Set this equal to zero to find the x-values which are not in the domain.
2Step 2: Solve the equation
To solve the equation \(\frac{3}{x}-1 = 0\), rearrange the equation to isolate x. This results in the equation \(x = \frac{3}{1}\). This indicates that x is not allowed to be 3 in the domain of h(x).
3Step 3: Formulate the domain of the function
Since x cannot be equal to 3 (derived from Step 2), the domain of h(x) is all real numbers except 3.
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