Math Challenges

Submissions for Problem #11

Problem #11

f is a function that takes real number x and performs the following three steps, in order. Find an expression for f(x). What is its domain?
1) Take the square root,
2) subtract 14,
3) make this quantity the denominator of a fraction, with 5 as the numerator

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zapwai

Solution: \( \displaylines{f\left(x\right)=\frac{5}{\sqrt{x}-14}\\ \left\lbrack0,14^2\right)\cup\left(14^2,\infty\right)} \)

Explanation:
I typically list each condition separately and then take the intersection of those constraints. In this case the presence of the square root (for real x) forces x >= 0. Being a fraction forces the denominator to not equal zero as well. So we just remove the singleton (x = 14^2) that would produce division by zero.

fish-face

Solution: \( \displaylines{\frac{5}{\sqrt{x}-14}\\ x\neq14^2\wedge x\geq0} \)

Explanation:
The codomain is not specified. If the function is intended to take values in the real numbers but be evaluated in the complex numbers, we can drop the second condition.