Give the domain of the following functions. Give your answer in interval notation. a) f(x)= 5x-2/x^2-5x+6 and b) square root of 5-2x

Answer 1

a. F(x) = (5x-2)/(x^2-5x+6)

F(x) = (5x-2)/(x-2)(x-3).
Any value of x that causes a zero
denominator is outside of the domain.

X = 2 and X = 3 will cause the denominator to be o. Therefore, they are outside of the domain.

Domain: All real values of X except 2, and 3.

b. Sqrt(5-2x).
Any value of X that causes the radical to go negative is outside the domain.

2x > 5.
X > 5/2
X > 2.5 is outside of domain.
Domain: X <= 2.5. Or 2.5 > X =2.5.