find domain of the definition y=log3(x2+1)/(sin2x - sinx + 0.25)
Given function is y = log3(x2 + 1)/(sin2x - sinx + 0.25)
Wkt, x2>= 0 which implies that x2+1 >= 1.
So, the expression in the numerator of the given function (i.e log3(x2 + 1)) is always defined for all real values of x.
Also, the denominator of the function should not be zero.
So, sin2x - sinx + 0.25 is not equal to zero.
i.e (sinx - 1/2)2 is not equal to zero.
i.e sinx must not be equal to 1/2.
which implies that x is not equal to n(pi) + (-1)n((pi)/6), where n is an integer.
So the domain of the function is R - {n(pi) + (-1)n((pi)/6) | n is an integer}.
Wkt, x2>= 0 which implies that x2+1 >= 1.
So, the expression in the numerator of the given function (i.e log3(x2 + 1)) is always defined for all real values of x.
Also, the denominator of the function should not be zero.
So, sin2x - sinx + 0.25 is not equal to zero.
i.e (sinx - 1/2)2 is not equal to zero.
i.e sinx must not be equal to 1/2.
which implies that x is not equal to n(pi) + (-1)n((pi)/6), where n is an integer.
So the domain of the function is R - {n(pi) + (-1)n((pi)/6) | n is an integer}.