+1995 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)
+129852 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
