Find the domain of the function. g(x)=5/5-4x. I think that it would read {x|x is a real number and x does not equal 5/4}.
I agree. I assume (5-4x) is the denominator.
5-4x=0 not allowed in denominator. -4x=-5 x=5/4d
To find the domain of a function, we need to consider the values of x for which the function is defined, or in other words, the values that can be plugged into the function without causing any issues.
In this case, we have the function g(x) = 5/(5 - 4x).
To determine the domain of this function, we need to look for any values of x that could lead to division by zero or any other mathematical issues.
For the given function, the only value of x that could potentially cause a problem is when the denominator, 5 - 4x, becomes zero. So, we need to solve the equation 5 - 4x = 0.
Rearranging this equation, we get 4x = 5, and dividing both sides by 4, we find x = 5/4.
Therefore, the only value of x that we need to exclude from the domain is x = 5/4. In interval notation, the domain of the function g(x) is (-∞, 5/4) ∪ (5/4, ∞).
Hence, your understanding is correct, and the domain of the function g(x) is {x | x is a real number and x is not equal to 5/4}.