What is the domain and range for #y = xcos^-1[x]#?
1 Answer
Range:
Domain:
Explanation:
#y' = arccos x - x / sqrt( 1 - x^2 ) = 0, at
y'' < 0, x > 0#. So,
Note that the terminal on the x-axis is [ 0, 1 ].
Inversely,
At the lower terminal,
and
Graph of
graph{y-x arccos x=0}
Graphs for x making y' = 0:
Graph of y' revealing a root near 0.65:
graph{y-arccos x + x/sqrt(1-x^2)=0[0 1 -0.1 0.1] }
Graph for 8-sd root = 0.65218462, giving
max y = 0.65218462( arccos 0.65218462 ) = 0.56109634:
graph{y-arccos x + x/sqrt(1-x^2)=0[0.6521846 0.6521847 -0.0000001 0.0000001]}