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Chapter 2: Problem 11

Find the key numbers of the expression. $$\frac{1}{x-5}+1$$

Short Answer

Expert verified
The key number of the expression \(\frac{1}{x-5}+1\) is \(x = 5\). There are no key numbers for which the expression equals zero.

Step by step solution

01

Identify where the function is undefined

An expression is undefined where the denominator is zero as division by zero is undefined in mathematics. In this case, \(x-5\) is in the denominator, therefore set \(x-5 = 0\). So, \(x = 5\) is a key number where the expression is undefined.
02

Find where the function equals zero

For an expression to be zero, the numerator must be equal to zero. Therefore, set the expression \(\frac{1}{x-5}+1\) equal to zero. Solving for \(x\) in this equality, we get no solution. Therefore, there are no key numbers for which the expression equals zero.

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