Question

Given f(x) = 2x – 4 and g(x) = x – 1, on which interval are both functions negative?

a (1, [infinity])
b (–[infinity], 1)
c (–[infinity], 2)
d (–[infinity], [infinity])

Answer 1

Both functions f(x) = 2x - 4 and g(x) = x - 1 are negative when x is < 1, so the interval on which both functions are negative is (–∞, 1).

Step-by-step explanation:

To determine on which interval both functions f(x) = 2x – 4 and g(x) = x – 1 are negative, we should find the x-values where each function is negative and then identify the overlapping interval.

For f(x):

2x - 4 < 0

2x < 4

x < 2

So, f(x) is negative when x is less than 2.

For g(x):

x - 1 < 0

x < 1

Therefore, g(x) is negative when x is less than 1.

Since g(x) becomes positive at a smaller value of x (1) than f(x), the interval where both functions are negative is when x is less than 1. Therefore, the correct interval is (–∞, 1), which matches option b.