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

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Answer 1 · 2017-12-02T10:35:32

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

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 $0<=y<=pi/4$ .

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