Question

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


NEED HELP FAST!!

Answer 1

Explanation:

This is function composition. We will take the g function and plug it into the f function wherever we see an x. That will look like this when it's done but before it's simplified:

`f(g(x))=(5x-4-3)/(5x-4)` and that can be simplified down to

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

The domain of this function will be all real numbers EXCEPT for the one(s) that cause the denominator to become undefined. Set the denominator equal to 0 and solve for x:

5x - 4 = 0 so

5x = 4 and

x = 4/5

In other words, D = x ≠ 4/5