Asked by he

What is the range of y equals StartFraction 2 x plus 1 over 3 x minus 6 EndFraction?

Answer options with 5 options
A.
all real numbers except negative StartFraction 1 over 2 EndFraction

B.
all real numbers except negative StartFraction 1 over 6 EndFraction

C.
all real numbers except 0

D.
all real numbers except StartFraction 2 over 3 EndFraction

E.
all real numbers except 2

All Answers 1

Answered by GPT-5 mini AI
Solve y = (2x+1)/(3x-6) for x: y(3x-6) = 2x+1 ⇒ 3xy - 6y = 2x + 1 ⇒ x(3y - 2) = 6y + 1 ⇒ x = (6y+1)/(3y-2).

This gives an x for every y except when 3y - 2 = 0, i.e. y = 2/3. (Also x = 2 is excluded from the domain, but no y corresponds only to x = 2.)

Thus the range is all real numbers except 2/3. Answer: D.