What Is The Range Of The Function F(x)=(5x-3)/(2x+1)? | Socratic

What is the range of the function #f(x)=(5x-3)/(2x+1)#? Algebra Expressions, Equations, and Functions Domain and Range of a Function

2 Answers

Narad T. Jul 26, 2017

The range is #y in RR-{5/2}#

Explanation:

#f(x)=(5x-3)/(2x+1)# Let

#y=(5x-3)/(2x+1)#

#y(2x+1)=5x-3#

#2yx+y=5x-3#

#5x-2yx=y+3#

#x(5-2y)=(y+3)#

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

The domain of #x=f(y)# is #y in RR-{5/2}#

This is also #f^-1(x)=(x+3)/(5-2x)#

graph{(5x-3)/(2x+1) [-22.8, 22.83, -11.4, 11.4]}

Answer link Jim G. Jul 26, 2017

#y inRR,y!=5/2#

Explanation:

#"given "y=(5x-3)/(2x+1)#

#"rearrange making x the subject"#

#rArry(2x+1)=5x-3larrcolor(blue)"cross-multiplying"#

#rArr2xy+y=5x-3larrcolor(blue)" distributing"#

#rArr2xy-5x=-3-ylarrcolor(blue)" collect terms in x"#

#rArrx(2y-5)=-(3+y)larrcolor(blue)" factor out x"#

#rArrx=-(3+y)/(2y-5)#

#"the denominator cannot equal zero as this would"# #"be undefined"#

#2y-5=0rArry=5/2larrcolor(red)" excluded value"#

#"range is "y inRR,y!=5/2#

Answer link

Related questions

• How do you determine if (-1, 4), (2, 8), (-1, 5) is a function?
• What is the domain for #f(x)=2x-4#?
• What is the domain and range for (3,1), (1,-4), and (2, 8)?
• What is the domain and range of a linear function?
• Is domain the independent or dependent variable?
• How do you find the domain and range of a function in interval notation?
• How do you find domain and range of a rational function?
• How do you find domain and range of a quadratic function?
• How do you determine the domain and range of a function?
• What is Domain and Range of a Function?

See all questions in Domain and Range of a Function

Impact of this question

3188 views around the world You can reuse this answer Creative Commons License