Pre calc question

Question

How do you find the domain / range for 5x-3/2-x

Answer 1

x can't = 2 as that makes the denominator = 0

domain is all x except 2: (-inf,2)U(2,inf)

from a graph range is about (-inf,2.2]U[17.8, inf)

to find the range take the derivative of 5x-3/(2-x) and set = 0, solve for x

to find the local max and min points. range is all y values greater than or equal to that maximum value

and less than or equal to that minimum point

y=5x-3/(2-x)

y' = 5 +3/(2-x)^2 = 0

multiply by (2-x)^2 to get

5(2-x)^2 -3 = 0

20-20x +5x^2 -3 =0

5x^2 -20x +17 = 0

x = about 1.2254, 2.7746= about 1.2, 2.8

plug them into f(x) to get about 17.8, 2.2