+0

+1
283
4
+1898

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
+1898
+1

im so confused

Dec 13, 2018
#2
+111325
+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

Dec 13, 2018
edited by CPhill  Dec 13, 2018
#3
+1898
+1

what about the (  ) do we need those

jjennylove  Dec 13, 2018
#4
+111325
0

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

log3 (x)  + 1

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

CPhill  Dec 13, 2018