Find the domain of the function.
h(x)= 10 over x^2 - 2x
I think the answer is all real numbers except 2 but I do not know if it is right!
the denominator factors to
x(x-2), so the restriction on x is 2 or 0
you had the "x is not equal to 2" correct
but notice when x = 0, the denominator is also zero.
To find the domain of a function, you need to determine which values of x make the function undefined. In this case, the function h(x) has a fraction with a denominator of x^2 - 2x. To find the values that make the denominator equal to zero, you can set it equal to zero and solve for x.
x^2 - 2x = 0
Factoring out an x, we get:
x(x - 2) = 0
Now we have two potential solutions:
x = 0
x - 2 = 0
Solving the second equation, we find:
x = 2
So, we have one value, x = 2, that makes the denominator equal to zero.
However, division by zero is undefined in mathematics, so x = 2 cannot be in the domain of the function h(x).
Therefore, the correct answer is that the domain of h(x) is all real numbers except x = 2.