range of sin(3x)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

implicit derivative tangent volume laplace fourier

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Steps Examples

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domain 2cos(x)

Solution

−∞ <x<∞

Interval Notation

(−∞ , ∞ )

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Solution steps

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Function range definition

The set of values of the dependent variable for which a function is defined

The function range is the combined domain of the inverse functions

Find the inverse function(s) of: (−3y)⁴

Inverse of (−3y)⁴: −⁴√y3 , ⁴√y3

−⁴√y3 , ⁴√y3

Find the domain of each inverse function

Domain of −⁴√y3 : y≥ 0

Domain of ⁴√y3 : y≥ 0

Combine the intervals

f(y)≥ 0

Solve instead

range 2cos(x)

periodicity 2cos(x)

amplitude 2cos(x)

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