What is the domain of f(x)=1+6sec^2(x/5) ?

The domain of f(x)=1+6sec^2(x/5) is 5pin<= x<(5pi)/2+5pin\lor (5pi)/2+5pin<x<5pi+5pin

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domain of f(x)=1+6sec^2(x/5)

domain

f (x) = 1 + 6 sec^{2} (\frac{x}{5})

5 πn \leq x < \frac{5 π}{2} + 5 πn or \frac{5 π}{2} + 5 πn < x < 5 π + 5 πn

Interval Notation

[5 πn, \frac{5 π}{2} + 5 πn) \cup (\frac{5 π}{2} + 5 πn, 5 π + 5 πn)

Solution steps

Take the denominator(s) of

1 + 6 sec^{2} (\frac{x}{5})

and compare to zero:

x = \frac{5 π}{2} + 5 πn

Periodicity of

1 + 6 sec^{2} (\frac{x}{5}) : 5 π

Combine period:

5 πn \leq x < 5 π + 5 πn

and undefined points.

The domain is

5 πn \leq x < \frac{5 π}{2} + 5 πn or \frac{5 π}{2} + 5 πn < x < 5 π + 5 πn

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

f (x) = \frac{( x - 3 )}{( x - 7 )}

x^{\frac{1}{3}}

f (x) = 2 + \frac{1 + x}{9 - x ^{2}}

f (x) = 2 x^{2} + 5 x - 4

What is the domain of f(x)=1+6sec^2(x/5) ?
The domain of f(x)=1+6sec^2(x/5) is 5pin<= x<(5pi)/2+5pin\lor (5pi)/2+5pin<x<5pi+5pin