If f(x)=x+7 and g(x)=1/x-13, what is the domain of (f x g)(x)?
Please explain.
To find the domain of the composite function (f x g)(x), we need to determine the values of x for which the function is defined.
First, let's understand the meaning of (f x g)(x). It represents the composition of the two functions f(x) and g(x) evaluated at x. So, (f x g)(x) can be written as f(g(x)).
Now, let's substitute g(x) into f(x) to get f(g(x)):
f(g(x)) = f(1/x - 13)
To find the domain, we need to consider two things:
1. The denominator in the definition of g(x) should not be zero.
2. The argument of the square root in f(g(x)) should not be negative (if there is a square root in f(x)).
Looking at the expression for g(x), we have 1/x - 13. To avoid a zero denominator, x cannot be equal to zero.
Next, we need to check for the argument of the square root in f(g(x)). However, there is no square root in the given function f(x) = x + 7.
Therefore, the domain of (f x g)(x) is all real numbers except x = 0 since the denominator in g(x) should not be zero.
In interval notation, the domain is (-∞, 0) U (0, +∞).
(f x g)(x) = (x+7)(1/x-13)
domain is the set of all real numbers except x = 0