Short Answer 
The process of combining functions involves creating a product function h(x) from f(x) and g(x), then applying the FOIL method to multiply the binomials. After simplifying the expression, it’s important to determine the domain by excluding any values that make the denominator zero, specifically avoiding x = 4/5.
Step 1: Combine the Functions
Start by combining the individual functions, f(x) and g(x), to form a new function denoted as (f*g)(x). This new function is essentially a product, which we can express as h(x). For this example, we have:
- h(x) = (x-3/x)(5x-4)
Step 2: Use the FOIL Method
Next, apply the FOIL (First, Outside, Inside, Last) method to multiply the two binomials present in the function. This step involves multiplying each term systematically to eliminate the parentheses and find a single polynomial expression. Make sure to perform this correctly to ensure accurate simplification.
- First: Multiply the first terms
- Outside: Multiply the outside terms
- Inside: Multiply the inside terms
- Last: Multiply the last terms
Step 3: Simplify and Set Domain
After applying FOIL, simplify the resulting expression as much as possible. The last step involves determining the domain of the function. It’s crucial to exclude any values that make the denominator zero; for this scenario, you avoid the value 4/5. Lastly, if your solved answer is a decimal, convert it into fraction form and round up if it’s non-terminating.
- Exclude x = 4/5 from the domain