Final answer:
The domain of the function 1/(9x-8) is all real numbers except for x = 8/9.
Step-by-step explanation:
The domain of the function 1/(9x-8) is all real numbers except for the values of x that make the denominator equal to zero. To find the values that make the denominator zero, we set 9x-8 = 0 and solve for x:
9x = 8
x = 8/9
So, the function is undefined at x = 8/9. Therefore, the domain is all real numbers except for x = 8/9.
The domain of the function in interval notation is (-∞, 8/9) ∪ (8/9, ∞).