What is the domain and range of #y = (arccos(x+3))/4#?

1 Answer
Dec 2, 2017

Answer:

The domain is #-4<=x<=-2# and the range is #0<=y<=pi/4#.

Explanation:

The ordinary domain and range of arccosine are
#-1<=x<=1# and #0<=y<=pi#, respectively.

The given function, #arccos(x+3)/4#, is shifted 3 units to the left and scaled by a factor of #1/4#.

The new domain is #-4<=x<=-2# (shifted 3 units to the left of the original) and the new range is #0<=y<=pi/4#.