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

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

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Answer 1 · 2017-12-02T10:35:32

The domain is $- 4 \leq x \leq - 2$ $-4<=x<=-2$ and the range is $0 \leq y \leq \frac{π}{4}$ $0<=y<=pi/4$ .

Explanation:

The ordinary domain and range of arccosine are
$- 1 \leq x \leq 1$ $-1<=x<=1$ and $0 \leq y \leq π$ $0<=y<=pi$ , respectively.

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

The new domain is $- 4 \leq x \leq - 2$ $-4<=x<=-2$ (shifted 3 units to the left of the original) and the new range is $0 \leq y \leq \frac{π}{4}$ $0<=y<=pi/4$ .

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

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