the function f is given by f(x) = cos⁻¹x. which of the following is the graph of y = f(x) in the xy - plane?
the function f is given by f(x) = cos⁻¹x. 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 $[0,\pi]$.
Step2: Analyze function behavior
The function $y=\cos^{-1}x$ is a decreasing function. When $x=-1$, $y = \cos^{-1}(-1)=\pi$; when $x = 1$, $y=\cos^{-1}(1)=0$.
Answer:
(No options are fully shown in the provided image, but based on the above - mentioned properties, the correct graph should have the domain $x\in[-1,1]$, range $y\in[0,\pi]$, and be a decreasing function from $(-1,\pi)$ to $(1,0)$)