the function $f$ is given by $f(x)=cos^{-1}x$. which of the following is the graph of $y = f(x)$ in the…
the function $f$ is given by $f(x)=cos^{-1}x$. which of the following is the graph of $y = f(x)$ in the $xy$-plane?
Answer
Explanation:
Step1: Recall domain and range of inverse - cosine function
The domain of (y = \cos^{-1}x) is ([- 1,1]) and the range is ([0,\pi]). Also, the function (y=\cos^{-1}x) is a decreasing function. When (x=-1), (y = \cos^{-1}(-1)=\pi); when (x = 1), (y=\cos^{-1}(1)=0).
Step2: Analyze the given options
Option A has a domain that seems correct but the function is increasing which is wrong for (y = \cos^{-1}x). Option B has the correct domain ([-1,1]), the correct range ([0,\pi]) and is a decreasing function.
Answer:
B.