Inverse functions?

[Kenny Pollock 10+ year member]

I'm taking class online... stuck on a problem, chapter didn't cover it too well.

Given f(x)=3x+4
1. Is f(x) a function? Why or why not?

2. Find f -1(x).

Is f -1(x) a function? Why or why not?

I understand the inverse function of (0,1) would be (1,0), etc. but how do I solve those questions? I'm asking for someone to teach me, not asking for someone to do my classwork.

Thanks!

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[JimJ 5,000+ posts]

IIRC, that question is asking you to do the "vertical line test" to determine whether something's a function or not. The idea being, for each unique value of X you put in, you get one value of Y back. If you have something that a vertical line will pass through twice, you have two values of Y for a given X.

So the answer to one would be yes, the answer to the second would be no.

Not sure if that's what they want...

 

[Beat_Dominator 5,000+ posts]

I remember doing that. If I can dig out my old math book I'll lern you some stuff.

 

[TIeclipseMOJO 10+ year member]

1. f(x) is a continous function because for any value of x there is a y value (example 3(2)+4=10 x is 2 y is 10

2. im not sure if this is correct but its my guess....

f(x) is the same as y. so f(x)=3x+4 is the same as y=3x+4 (the equation of a line)

if you switch x and y you get x=3y+4.... solving for y you get y = (x-4)/3

which 3.) should still be a function

not 100% positive but hope that helps

 

[Kenny Pollock 10+ year member]

Thank you Jim, I keep forgetting f(x) is the same thing as y. If I replace it with a y, I see I should graph it. Why is y "no"? I don't understand the second problem.

 

[Tiger Bass 5,000+ posts]

To find the inverse function, literally replace the x with y.

Ex. y=3x+4

x=3y+4

Now solve for the y.

y=(x-4)/3

 

[Kenny Pollock 10+ year member]

Tiger: Maybe I'm reading into it to much? From what you put down, I still can't tell if it's a function or not... mind explaining to a math n00b?

 

[JimJ 5,000+ posts]

Eh, never did too well in precal anyway...

Somebody want to help me calculate adjusted exponential smoothing values for some data?

//content.invisioncic.com/y282845/emoticons/biggrin.gif.d71a5d36fcbab170f2364c9f2e3946cb.gif

 

[TIeclipseMOJO 10+ year member]

Tiger: Maybe I'm reading into it to much? From what you put down, I still can't tell if it's a function or not... mind explaining to a math n00b?

yes its still a function y=(x-4)/3 graph that you will see its just a diagonal line slope of 1/3 y interecept of -4/3 therefore it passes the vertical line test. got a graphing calculator or have to plot points by hand?

 

[Kenny Pollock 10+ year member]

I messed up in Algebra II first semester... retaking it online for a chance to up my GPA //content.invisioncic.com/y282845/emoticons/frown.gif.a3531fa0534503350665a1e957861287.gif

 

[Kenny Pollock 10+ year member]

yes its still a function y=(x-4)/3 graph that you will see its just a diagonal line slope of 1/3 y interecept of -4/3 therefore it passes the vertical line test. got a graphing calculator or have to plot points by hand?

AH, again, owned by not graphing.

I have a TI-89 Titanium in front of me... doh

Thanks guys //content.invisioncic.com/y282845/emoticons/smile.gif.1ebc41e1811405b213edfc4622c41e27.gif

 

[Tiger Bass 5,000+ posts]

JimJ is right for the second part. You use the vertical line test to make sure its a function. Basically, you take a plot and if you can draw a line veritcally through the plot and it only passed through it once, its a function.

 

[ballstothewall 10+ year member]

Tiger: Maybe I'm reading into it to much? From what you put down, I still can't tell if it's a function or not... mind explaining to a math n00b?

To tell if its a function, graph it (use a calculator) and see if it passes the vertical line test. If a line going vertical only intersects the function at one place, its a function. If at ANY point on the graph it intersects at two points, it fails the test.

Tiger just told you how to determine the inverse function per your thread topic.

*edit* I'm to slow.

 

[TIeclipseMOJO 10+ year member]

ah i have the ti 89 titanium also... actually dont like it very much. liked the 83 more for graphing. untill i got to calc I II and III... 89 does derivatives and intergrals FTW so if you have to go any further in math keep the 89

 

[lilmaniac2 5,000+ posts]

i miss high school algebra

anybody care to help explain to me how one infinity could be bigger than another ?