What is the domain of f(x)=tan(pi/4 x) ?

The domain of f(x)=tan(pi/4 x) is 4n<= x<2+4n\lor 2+4n<x<4+4n

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domain of f(x)=tan(pi/4 x)

domain

f (x) = tan (\frac{π}{4} x)

4 n \leq x < 2 + 4 n or 2 + 4 n < x < 4 + 4 n

Interval Notation

[4 n, 2 + 4 n) \cup (2 + 4 n, 4 + 4 n)

Solution steps

Take the denominator(s) of

tan (\frac{π}{4} x)

and compare to zero:

x = 2 + 4 n

Periodicity of

tan (\frac{π}{4} x) : 4

Combine period:

4 n \leq x < 4 + 4 n

and undefined points.

The domain is

4 n \leq x < 2 + 4 n or 2 + 4 n < x < 4 + 4 n

\frac{x - 1}{5 - x}

lo g_{3} (x - 5) + 1

f (t) = 2 t^{2} + 5 t - 3

- \frac{4 x}{( x - 7 ) ( x + 5 )}

f (x) = - 1 x^{2} + 4

What is the domain of f(x)=tan(pi/4 x) ?
The domain of f(x)=tan(pi/4 x) is 4n<= x<2+4n\lor 2+4n<x<4+4n