How do you find the domain and range for #y = (3(x-2))/x#?

2 Answers
Jun 29, 2018

Answer:

Domain : #x < 0 " or" x > 0#

Range : -6 / (x - 3)#

Explanation:

The domain is the set of all possible x-values which will make the function "work", and will output real y-values.

Find the domain and range of the function y = 1 x + 3 − 5 . To find the excluded value in the domain of the function, equate the denominator to zero and solve for .

The range of the function is same as the domain of the inverse function.

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

Domain : When x = 0, point x=0 is undefined.

The function domain #x < 0 " or " x > 0#

Range : Set of values of the dependent variable for which a function is defined.

Function range is the combined domain of the inverse functions.

#"inverse of " (3(x-2))/x : - 6/(x-3)#

graph{(3 (x - 2)) / x [-10, 10, -5, 5]}

Jun 29, 2018

Answer:

#x inRR,x!=0,y inRR,y!=3#

Explanation:

The denominator of y cannot be zero as this would make y undefined. Equating the denominator to zero and solving gives the value that x cannot be.

#x=0larrcolor(red)"excluded value"#

#"domain is "x inRR,x!=0#

#(-oo,0)uu(0,oo)larrcolor(blue)"in interval notation"#

#"to find the range, rearrange making x the subject"#

#xy=3x-6#

#xy=3x=-6#

#x(y-3)=-6#

#x=-6/(y-3)#

#"solve "y-3=0rArry=3larrcolor(red)"excluded value"#

#"range is "y inRR,y!=3#

#(-oo,3)uu(3,oo)#
graph{(3x-6)/x [-20, 20, -10, 10]}