Find the Domain and Range f(x)=2sin(2x)-pi/2

$f (x) = 2 \sin (2 x) - \frac{π}{2}$

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:

$[- 2 - \frac{π}{2}, 2 - \frac{π}{2}]$

Set-Builder Notation:

${y | - 2 - \frac{π}{2} \leq y \leq 2 - \frac{π}{2}}$

Step 3

Determine the domain and range.

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

Range: $[- 2 - \frac{π}{2}, 2 - \frac{π}{2}], {y | - 2 - \frac{π}{2} \leq y \leq 2 - \frac{π}{2}}$

Step 4

Find the Domain and Range f(x)=2sin(2x)-pi/2

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