find two functions f and g such that (f+g)(x) = 5 and domain of f + g is [0, infinity)
Try something like
f(x) = 2 + sqrt(x)
g(x) = 3 - sqrt(x)
f+g = 5, but they are only defined for x>=0
Why did the function go to the circus? Because it wanted to perform an addition act!
Alright, let's find two functions that satisfy your conditions. How about f(x) = 6 - x and g(x) = -1?
If we add them together, (f+g)(x) = f(x) + g(x) = (6 - x) + (-1) = 5.
And the domain of f + g is [0, infinity) since both f and g have domains of [0, infinity).
So there you have it! The magical duo for (f+g)(x) = 5 and the domain of f + g being [0, infinity) is f(x) = 6 - x and g(x) = -1.
To find two functions with the given conditions, we need two functions whose sum equals a constant and the domain of their sum is [0, infinity).
Let's define f(x) = 5 - x and g(x) = x.
Now, let's verify if these functions satisfy the conditions:
(f+g)(x) = f(x) + g(x) = (5 - x) + x = 5
So, the sum of f and g is indeed 5.
Now let's check the domain of their sum. The domain of f(x) is [0, infinity) and the domain of g(x) is also [0, infinity). Since both functions have the same domain and their sum only includes addition operations, the domain of the sum, (f+g)(x), will also be [0, infinity).
Therefore, the functions f(x) = 5 - x and g(x) = x satisfy the given conditions.
To find two functions f and g such that (f + g)(x) = 5 and the domain of f + g is [0, infinity), we need to follow these steps:
1. Define a function f(x) that satisfies the given domain [0, infinity):
- Let's choose f(x) = 4, a constant function that always yields 4 for any x in the given domain [0, infinity).
2. Now, we need to find the function g(x) that, when added to f(x), results in 5 for any x in the domain [0, infinity). Since f(x) is a constant function equal to 4, g(x) must be a function that, when added to 4, gives a sum of 5. In other words, g(x) = 5 - f(x).
Therefore, the functions f(x) = 4 and g(x) = 5 - f(x) satisfy the given conditions.
To verify this:
- For any x in the domain [0, infinity), the sum of f(x) + g(x) would be:
f(x) + g(x) = 4 + (5 - 4) = 5.
Hence, (f + g)(x) = 5, and the domain of f + g is [0, infinity).