What is the domain of f(x)= 1/(1-cos^2(x-3/2)) ?

The domain of f(x)= 1/(1-cos^2(x-3/2)) is pin<= x< 3/2+pin\lor 3/2+pin<x<pi+pin

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domain of f(x)= 1/(1-cos^2(x-3/2))

domain

f (x) = \frac{1}{1 - cos ^{2} ( x - \frac{3}{2} )}

πn \leq x < \frac{3}{2} + πn or \frac{3}{2} + πn < x < π + πn

Interval Notation

Solution steps

Take the denominator(s) of

\frac{1}{1 - cos ^{2} ( x - \frac{3}{2} )}

and compare to zero:

x = \frac{3}{2} + πn

Periodicity of

\frac{1}{1 - cos ^{2} ( x - \frac{3}{2} )} : π

Combine period:

πn \leq x < π + πn

and undefined points.

The domain is

πn \leq x < \frac{3}{2} + πn or \frac{3}{2} + πn < x < π + πn

\frac{x + 8}{3}

y = - (0.02)^{x + 6}

g (x) = \frac{x - 2}{x - 4}

\frac{4 x + 9}{3 x - 4}

f (x) = lo g_{10} (- x - 20)

What is the domain of f(x)= 1/(1-cos^2(x-3/2)) ?
The domain of f(x)= 1/(1-cos^2(x-3/2)) is pin<= x< 3/2+pin\lor 3/2+pin<x<pi+pin