+0  
 
+1
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avatar+393 

What is the inverse of the function?

f(x)=3x-1

 

f−1(x)=log3(x)−1

 

f−1(x)=log3(x)+1

 

f−1(x)=log3(x+1)

 

f−1(x)=log3(x−1)

 Dec 13, 2018
edited by Guest  Dec 13, 2018
 #1
avatar+393 
+1

im so confused

 Dec 13, 2018
 #2
avatar+94526 
+1

The idea, at first, is to get x by itself

 

Let's write this

 

y = 3^(x - 1)       take the log of both sides

 

log y = log 3^(x - 1)     and we can write

 

log y = (x - 1) log 3      divide both sides by log 3

 

[ log y  ] / [log 3]  = x - 1      add 1 to both sides

 

[ log y ] / [ log 3]  + 1  =  x       now,  "swap" x and y

 

[log x] / [log 3] + 1  =   y           

 

By the change of base theorem,  [ log x ] / [ log 3]  =  log3 (x)

 

So we have

 

log3 (x)  + 1  =  y  =  f-1(x)         and this is the inverse

 

 

cool cool cool

 Dec 13, 2018
edited by CPhill  Dec 13, 2018
 #3
avatar+393 
+1

what about the (  ) do we need those

jjennylove  Dec 13, 2018
 #4
avatar+94526 
0

Sorry Jenny.....yes... it should be

 

log3 (x)  + 1

 

I'll make that correction....thx for pointing that out....it's important  !!!

cool cool cool

CPhill  Dec 13, 2018

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