Answer:
Step-by-step 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:
[tex]f(g(x))=\frac{5x-4-3}{5x-4}[/tex] and that can be simplified down to
[tex]f(g(x))=\frac{5x-7}{5x-4}[/tex]
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 | x ≠ 4/5}
