Let f(x) = 2x-1 and g(x) = 4-x. Find all values of x for which f(x) < -1 or g(x) <3. solution set in interval notation.
(-∞,0) ∪ (1,∞)
To find all values of x for which f(x) < -1 or g(x) < 3, we need to solve each inequality separately and then combine the solution sets.
1. Solving f(x) < -1:
Substitute f(x) = 2x - 1 into the inequality:
2x - 1 < -1
Add 1 to both sides:
2x < 0
Divide both sides by 2:
x < 0.
So, the solution to f(x) < -1 is x < 0.
2. Solving g(x) < 3:
Substitute g(x) = 4 - x into the inequality:
4 - x < 3
Subtract 4 from both sides:
-x < -1
Multiply both sides by -1 (remember to flip the inequality when multiplying by a negative number):
x > 1.
So, the solution to g(x) < 3 is x > 1.
Now, combining the solution sets, we have x < 0 or x > 1.
In interval notation, we can represent x < 0 or x > 1 as the union of two intervals: (-∞, 0) U (1, ∞).