Question

Let f(x) = 1/x and g(x) = x^2 + x. What two numbers are not in the domain of fog?

Options:
a) 0, -1
b) 0, 1
c) 1, -1
d) 1, 0

Answer 1

The numbers 0 and -1 are not in the domain of the composite function fog(x), as they cause the denominator in the function f(x) = 1/x to be zero, making the composite function undefined.

Step-by-step explanation:

To find which two numbers are not in the domain of fog(x), which means the composite function f(g(x)), we must first identify the individual domains of f(x) and g(x). The function f(x) = 1/x is undefined when x is 0 because division by zero is not allowed. The function g(x) = x² + x can take any real number as input. However, for the composite function f(g(x)), any value of x that makes g(x) equal to 0 leads to an undefined value in function f(x). We solve the equation g(x) = 0, which is x² + x = 0, by factoring out x to get x(x + 1) = 0. This gives us two values: x = 0 and x = -1. Therefore, the two numbers not in the domain of fog(x) are 0 and -1.