Question

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).

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Answer 1

`f(x) = (x - 25)/(5x - 5)`

Domain:
`x \\e 1`

Explanation:

Given

`f(5x) = (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) = ((5x)/(5) - 5)/(5x - 1)`

`f(x) = ((x)/(5) - 5)/(x - 1)`

Take LCM

`f(x) = ((x - 25)/(5))/(x - 1)`

`f(x) = (x - 25)/(5) * (1)/(x-1)`

`f(x) = (x - 25)/(5x - 5)`

To get the domain, we set the denominator as

`5x - 5 \\e 0`

`5x \\e 5`

`x \\e 1`