I have no idea how to do this, and nobody in my family knows how to either.
I have to determine the domain of the following function.
f(x)=5/(3x-7)
the domain is where the function is defined.
Since it's just a fraction, it is defined for all real values of x.
EXCEPT that division by zero is not defined.
So, if 3x-7 = 0 then f(x) is undefined.
So, the domain is all real numbers except 7/3
Determining the domain of a function involves identifying all the possible values for which the function is defined. In the case of the given function, f(x) = 5/(3x-7), there is a restriction that needs to be considered.
The domain of this function is all the values that x can take while ensuring that the denominator, 3x-7, does not become zero. This is because division by zero is undefined in mathematics.
To find the values of x that make the denominator zero, we set 3x-7 equal to zero and solve for x:
3x - 7 = 0
Adding 7 to both sides:
3x = 7
Dividing both sides by 3:
x = 7/3
So, x can take any value except x = 7/3.
Therefore, the domain of the given function is all real numbers except x = 7/3.