Question

If f(x)=x-3/x and g(x)=5x-4, what is the domain of (f•g)(x)

Answer 1

basically C

Explanation:

Answer 2

`\x\\eq (4)/(5)\`

Explanation:

Given functions are,

`f(x)=(x-3)/(x)-----(1)`

`g(x)=5x-4-----(2)`

Now, by the property of composition of functions,

`(fog)(x)=f(g(x))`

`=f(5x-4)` ( From equation (2) )

`=(5x-4-3)/(5x-4)` ( From equation (1) )

`=(5x-7)/(5x-4)`

Which is a rational function,

Since, the rational function is defined for all real numbers except those real values for which denominator = 0,

If 5x - 4 = 0

`\implies x = (4)/(5)`

So, the function (fog) is defined for all real numbers except 4/5,

Therefore, the domain of (fog)(x) is
`\x\\eq (4)/(5)\`.