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# Functions

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Given f(x) = sqrt((x - 7)/(4 - x)), what is the smallest possible integer value for x such that f(x) has a real number value?

May 17, 2022

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If f(x) has a real number value,

$$\dfrac{x - 7}{4 - x} \geq 0\\ (x - 7)(4 - x) \geq 0\text{ and }x \neq 4\\ 4 < x \leq 7$$

The smallest possible integer in that range is x = 5.

May 18, 2022