Draw the graph of cos−1x, where x∈[−1,0]. Also write its range.
Answer: Range =[2π,π]; graph is the decreasing arc from (−1,π) to (0,2π).
Solution
y=cos−1x is a decreasing function. On the restricted domain x∈[−1,0] its end values are
cos−1(−1)=π,cos−1(0)=2π
As x increases from −1 to 0, y decreases continuously from π to 2π, so the curve is the upper-left portion of the full cos−1 graph. Hence the range for x∈[−1,0] is
[2π,π]
(See the accompanying figure: a smooth decreasing curve from (−1,π) to (0,2π).)
