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

Question

asked Jul 14, 2019 203k views

2 Answers

Eduard · Answer 1 · 2019-07-21T05:18:21+0000

Answer:

$\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)\$ .