Question

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

Answer 1

to sum it up, its C

Explanation:

took the test

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}`