Question 1170514: Functions f and g are given by
f(x)=12x−7 and g(x)=123x−41
Simplify (f∘g)(x).
(f∘g)(x)=
List the numbers that are NOT in the domain of f∘g in a comma separated list.
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's find (f∘g)(x) and its domain.
**1. Find (f∘g)(x)**
(f∘g)(x) = f(g(x))
We have:
f(x) = 12x - 7
g(x) = 123x - 41
Substitute g(x) into f(x):
(f∘g)(x) = f(123x - 41)
(f∘g)(x) = 12(123x - 41) - 7
(f∘g)(x) = (12 * 123)x - (12 * 41) - 7
(f∘g)(x) = 1476x - 492 - 7
(f∘g)(x) = 1476x - 499
**2. Find the Domain of (f∘g)(x)**
* The domain of f(x) = 12x - 7 is all real numbers, since it's a linear function.
* The domain of g(x) = 123x - 41 is also all real numbers, since it's a linear function.
* The composition (f∘g)(x) = 1476x - 499 is also a linear function, so its domain is all real numbers.
Since both f(x) and g(x) have a domain of all real numbers, the composition (f∘g)(x) also has a domain of all real numbers.
**3. List Numbers NOT in the Domain**
Since the domain of (f∘g)(x) is all real numbers, there are no numbers excluded from the domain.
**Answer:**
(f∘g)(x) = 1476x - 499
List the numbers that are NOT in the domain of f∘g in a comma separated list: None
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