Question

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

Answer 1

Answer:

$\{x|x\neq \frac{4}{5}\}$

Step-by-step explanation:

Given functions are,

$f(x)=\frac{x-3}{x}-----(1)$

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

Now, by the property of composition of functions,

$(fog)(x)=f(g(x))$

$=f(5x-4)$    ( From equation (2) )

$=\frac{5x-4-3}{5x-4}$   ( From equation (1) )

$=\frac{5x-7}{5x-4}$

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

$\implies x = \frac{4}{5}$

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

Therefore, the domain of (fog)(x) is $\{x|x\neq \frac{4}{5}\}$.

Answer 2

Log number 1 find catalog 5 - 4 = 1 . ( f .g ) 1 log = 0