What is the domain of f(x)=1+tan((pix)/4) ?

The domain of f(x)=1+tan((pix)/4) is 4n<= x<2+4n\lor 2+4n<x<4+4n

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domain of f(x)=1+tan((pix)/4)

domain

f (x) = 1 + tan (\frac{π x}{4})

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

1 + tan (\frac{π x}{4})

and compare to zero:

x = 2 + 4 n

Periodicity of

1 + tan (\frac{π x}{4}) : 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

x^{7} - 3

f (x) = \frac{1}{x - 25}

9 x + 1

y = \frac{x ^{2} - 1}{x ^{2} - 4}

f (x) = \frac{2 x + 3}{- 5 x - 53}

What is the domain of f(x)=1+tan((pix)/4) ?
The domain of f(x)=1+tan((pix)/4) is 4n<= x<2+4n\lor 2+4n<x<4+4n