Find the domain of the function. f(x) = 1/4 * tan(4x)

Answer 1

tanθ is defined as long as θ ≠ π/2 + kπ, where k = 0, ±1, ±2, ...

So, tan(4x) is defined only when 4x ≠ π/2 + kπ

Domain = { x l x ≠ π/8 + kπ/4}

Answer 2

domain is all values of x that do not make f(x) undefined

tan4x is not defined for 4x=pi/2 or 3pi/2 + 2npi

x cannot =pi/8 +2npi, or 3pi/8 +npi/2 where n=any integer..

x cannot = pi/8 +npi/2

domain is all other angles

or

in degrees

x cannot = 180/8, 270/8, 180/8+/-90, 270/8+/-90,...

= 22.5, 67.5, 112.5, 157.5, ...

or -22.5, -67.5, -112.5, -157.5, ...

x cannot = 22.5 +45n where n= any integer

assuming you meant f(x)= (1/4)tan(4x)

and not f(x)= 1/(4tan4x)

if you meant the latter, then

4x cannot = 0 or pi

x cannot = 0 or pi/4 + npi/4 as they make the denominator = 0

x cannot = npi/4 radians where n = any integer