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AlekseyPX
3 years ago
6

Consider a function f(x) such that f(5x) =x-5/5x-1. Find f(x) and hence write down the domain of f(x).

Mathematics
1 answer:
nasty-shy [4]3 years ago
4 0

Answer:

f(x) = \frac{x - 25}{5x - 5}

Domain: x \ne 1

Step-by-step explanation:

Given

f(5x) = \frac{x - 5}{5x - 1}

Required

Determine f(x) and its domain

To determine f(x), we replace 5x with x in f(5x)

So, we have:

f(5x) = \frac{\frac{5x}{5} - 5}{5x - 1}

f(x) = \frac{\frac{x}{5} - 5}{x - 1}

Take LCM

f(x) = \frac{\frac{x - 25}{5}}{x - 1}

f(x) = \frac{x - 25}{5} * \frac{1}{x-1}

f(x) = \frac{x - 25}{5x - 5}

To get the domain, we set the denominator as

5x - 5 \ne 0

5x \ne 5

x \ne 1

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