Question

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

Answer 1

You must plug the g(x) function into every x in f(x)...

((5x)-3)/(5x) = (fog)(x)

Since the only value that would be undefined is x = 0 which makes the denominator zero, the domain is all reals except x = 0.

Or

(−∞,0)U(0,∞)

Answer 2

For this case we have the following functions:

$f (x) = \frac {x - 3} {x}\\g (x) = 5x - 4$

The first thing we should do is the composition of functions.

We have then:

$f (g (x)) = \frac {(5x - 4) - 3} {5x - 4}$

Rewriting we have:

$f (g (x)) = \frac {5x - 7} {5x - 4}$

Therefore the domain of the function are the values of x that define the function.

The function is not defined for:

$5x - 4 = 0\\5x = 4\\x = \frac {4} {5}$

Answer:

The domain of the function is:

All real numbers except $\frac {4} {5}$