Solve the inequality.x/3-x-1/2≥1 a. x≤-3 b. x≥-3 c. x≤3 d. x≥3
1 answer:
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Answer:
The first choice, .
Step-by-step explanation:
The dashed vertical line is a vertical asymptote. The x-coordinate of all points on this vertical asymptote are equal to 7. In other words, when the x-value of a point on the graph approaches , its y-value approaches infinity (or negative infinity.)
Either way, the graph is not defined for . The point
should thus be excluded from the domain of the graph.
The graph is apparently defined for all other x-values. The domain of the function should thus be all real numbers with the exception of . Here's how to write that in interval notation:
- The set of all real numbers can be expressed as the interval
. Note that infinity
(or
itself isn't a real number. The round brackets indicate that both endpoints are excluded from the from the interval.
- The set of all real numbers less than (not equal to)
is
(both ends are excluded.) The set of all real numbers greater than (not equal to)
.
- The set of all real numbers that is not equal to
connects two intervals.
In other words, the domain is .
