Problem 64
Question
Find the domain of the function. $$h(x)=\frac{10}{x^{2}-2 x}$$
Step-by-Step Solution
Verified Answer
The domain of the given function is all real numbers except \(x=0\) and \(x=2\).
1Step 1: Identify the Denominator
Our first step is to identify the denominator of the function, which is \(x^{2}-2 x\).
2Step 2: Set the Denominator Equal to Zero
We need to find which x-values make the denominator equal to zero. To do so, we set the denominator equal to zero. So, we solve the equation \(x^{2}-2 x=0\).
3Step 3: Solve for x
Factor x out of the equation to get \(x*(x-2)=0\). This equation equals zero if either of the factors equals zero. Therefore, we set \(x=0\) and \(x-2=0\) and solve for x in each case. The solutions are \(x=0\) and \(x=2\).
4Step 4: Exclude these values from the domain
Finally, the values obtained should be excluded from the domain of the function since these make the denominator zero. Hence, the domain of the function \(h(x)=\frac{10}{x^{2}-2 x}\) is all real numbers excluding \(x=0\) and \(x=2\).
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