Inverse function of log12(x)

[csprin1]

I am working on a revision and I keep getting that its right but my work is wrong. This is my work:


I have no idea what I am doing wrong, I am not extremely strong with inverse function. Any help as to what I am doing wrong would be gratefully appreciated.

 

[csprin1]

correction

Is this better?

 

[DrPhil]

Is this better?

View attachment 3141

At step 2 you are just to exchange symbols - not the operations

1) \(\displaystyle y = f(x) = log_{12}x \)...,,the domain of this function is \(\displaystyle x > 0\)

2) \(\displaystyle x = log_{12}y \)...,,the domain of this function is \(\displaystyle y > 0\), range \(\displaystyle x \in \Re\)

3) \(\displaystyle log_{12}y = x \implies y = 12^x \)...,,the domain of this function is \(\displaystyle x \in \Re\)

4) \(\displaystyle f^{-1}(x) = 12^x\)...,,the domain of this function is \(\displaystyle x \in \Re\)

I don't see anything wrong - what is it "supposed" to be?

 

[csprin1]

This was my revision, my first attempt (I did not post here) was completely wrong. I just wanted to make sure that the work shown was correct.

 

[DrPhil]

This was my revision, my first attempt (I did not post here) was completely wrong. I just wanted to make sure that the work shown was correct.

ok - just be a little more careful with the "switch." After x and y are interchanged, don't keep the old form around. And sometimes you may want to keep track of range and domain, which also switch.