Let f(x) = x – 4 and g(x) =1/x. The graph of (gºf)(x) is shown below. What is the domain
Mathematics · Middle School · Tue Nov 03 2020
Answered on
Given:
f(x) = x - 4
g(x) = 1/x
Determine the domain of (gºf)(x)
Explanation:
We can easily determine the domain of the given function without the need of a graph, simply by solving first (gºf)(x).
(gºf)(x) = 1 / (x -4)
In order to determine the domain of rational function, we equate the denominator to 0, and solve for x.
x - 4 = 0
Transpose -4 on the other side of the equation, note that when transposing a number, the sign changes.
x = 4
Domain: Set of real numbers except for x = 4
x cannot be equal to 4 since the denominator will be 0, and having 0 in the denominator means that the function does not exist.
Final answer:
Domain: Set of real numbers except for x = 4