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).

The domain of is .

Step-by-step explanation:

Let , which is rearranged by algebraic means:

1)  Given

2) Modulative property

3) Existence of multiplicative inverse/Associative and commutative properties.

4) Composition of functions.

5) Existence of multiplicative inverse/Associative property.

6)  Commutative, associative and distributive properties//Definition of subtraction

7) Definition of division/Associative property

8)  /Distributive property//Definition of subtraction

9) Definition of division/Result

The domain of a polynomial-based rational function consists in all values of the real set except values where denominator equals zero. The value of such that rational function becomes undefined is:

1)  Given

2) Distributive property

3) Compatibility with multiplication

4) Commutative and associative properties/

5) Existence of multiplicative inverse/Modulative property

6) Compatibility with addition/Commutative and associative properties

7) Existence of additive inverse/Modulative property/Result

Hence, the domain of is .