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Chapter 1: Problem 56

Find the domain of the function. $$h(x)=\frac{10}{x^{2}-2 x}$$

Short Answer

Expert verified
The domain of \(h(x) = \frac{10}{x^2 - 2x}\) is \((-鈭�, 0) \cup (0, 2) \cup (2, 鈭�)\)

Step by step solution

01

Find where the denominator equals zero

Set the denominator equal to zero and solve for \(x\). This will find the values where the function is undefined. So we set \(x^2 - 2x = 0\)
02

Factor the equation

The equation from Step 1 can be factored to give \(x(x - 2) = 0\)
03

Solve for x

Setting each factor equal to zero gives the solutions \(x = 0\) and \(x = 2\)
04

Determine the domain of function

The domain of the function is all real numbers except \(x = 0\) and \(x = 2\). In interval notation, this is \((-鈭�, 0) \cup (0, 2) \cup (2, 鈭�)\)

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