I don't understand how to do this problem, can you please help me?
Given the functions f and g, determine the domain of f+g.
4. f(x)= 2x/(x-3) g(x)=3/(x+6)
That would be the set of real numbers x that result in real values for f + g
For f(x) by itself, the domain is all numbers except 3. For g(x), the domain is all numbers except -6.
For f + g, the domain is all numbers from -infinity to +infinity except -6 and 3.
For further reading I suggest
http://www.analyzemath.com/DomainRange/DomainRange.html
To find the domain of the sum of two functions, f(x) + g(x), we need to consider the restrictions on the individual functions and identify any values that would make the sum undefined.
First, let's consider the restrictions on the function f(x) = 2x / (x - 3). In this case, the function is undefined when the denominator (x - 3) equals zero, since division by zero is undefined. So, we need to exclude the value x = 3 from the domain of f(x).
Now, let's consider the restrictions on the function g(x) = 3 / (x + 6). Similarly, this function is undefined when the denominator (x + 6) equals zero. So, we need to exclude the value x = -6 from the domain of g(x).
To determine the domain of the sum f(x) + g(x), we need to find the common domain in which both f(x) and g(x) are defined. Since the only restricted values are x = 3 and x = -6, the sum f(x) + g(x) will be defined for all other values of x.
Therefore, the domain of f(x) + g(x) is all real numbers except x = 3 and x = -6. In interval notation, the domain can be expressed as (-∞, -6) U (-6, 3) U (3, +∞).