Find the Domain and Range y=7arctan(3x)

$y = 7 \arctan (3 x)$

Step 1

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 2

The range is the set of all valid $y$ values. Use the graph to find the range.

Interval Notation:

$(- \frac{7 π}{2}, \frac{7 π}{2})$

Set-Builder Notation:

${y | - \frac{7 π}{2} < y < \frac{7 π}{2}}$

Step 3

Determine the domain and range.

Domain: $(- \infty, \infty), {x | x \in ℝ}$

Range: $(- \frac{7 π}{2}, \frac{7 π}{2}), {y | - \frac{7 π}{2} < y < \frac{7 π}{2}}$

Step 4

Find the Domain and Range y=7arctan(3x)

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