Find f(g(x)). State the domain of the composite function.
f(x) = 3x-2/x+1
g(x) = x+5/2x-3

ℝ - {(-2/3),(3/2)}

Step-by-step explanation:

We want the domain of f(g(x)). So, firstly, we have to find the domain for g(x) and, then, for f(g(x)).

- Domain of g(x): Since the expression is a fracion, we must exclude the values of x that make null the denominator. Hence,

- Domain of f(g(x)): We'll find its expression:

Now, once again, we have to exclude the values of x that make the denominator equals to zero. Thus,

Lastly, we may write the domanin of f(g(x)):

or, just writing in a shorter way:

for ex: the reciprocal of 3/4 is 4/3. it is the opposite.

reciprocal definition:

a mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.