Could you please help in finding the domain? Thanxs!
Find the domain of the function.
g(x)= 3x/(x^2 -49)
To find the domain of the function g(x) = 3x/(x^2 - 49), we need to determine the values of x for which the function is defined.
The function is undefined if the denominator, x^2 - 49, equals zero because we cannot divide by zero. So, we set the denominator equal to zero and solve for x:
x^2 - 49 = 0
To solve this equation, we can factor it as the difference of squares:
(x - 7)(x + 7) = 0
Now, we can set each factor equal to zero and solve for x:
x - 7 = 0 --> x = 7
x + 7 = 0 --> x = -7
These values, x = 7 and x = -7, make the denominator equal to zero. Therefore, they are not in the domain of the function g(x).
Since the only values of x that are excluded from the domain are x = 7 and x = -7, we can say that the domain of the function g(x) = 3x/(x^2 - 49) is all real numbers except x = 7 and x = -7.