Find the domain of the function
g(x)= 4/3-5x I am sorry this is a fraction
No problem! To find the domain of a function, we need to determine the values that x can take which will not result in any undefined or forbidden operations. In this case, we need to ensure that the denominator of the fraction, which is 3 - 5x, is not equal to zero, since division by zero is undefined.
To find the values of x that make the denominator equal to zero, we can set it equal to zero and solve for x:
3 - 5x = 0
To solve for x, we will isolate it by moving the constant term to the other side:
5x = 3
Dividing both sides by 5, we obtain:
x = 3/5
Therefore, the value x = 3/5 is the only value that would make the denominator zero. Hence, the domain of the function g(x) = 4/(3 - 5x) is all real numbers except x = 3/5. In interval notation, it can be written as (-∞, 3/5) U (3/5, +∞).