The Student Room Group

C3 inverse function

I have to show that

f(x) = ln (4x-2)

can be defined as

f^-1(x) = 2 - (1/2)e^x

First of all, I started by swapping x and y around and then rearranged the equation.

y=ln(4x-2)

x=ln(4y-2)

e^x= 4y-2

e^x +2 =4y

(e^x+2)/4=y

I'm not sure where I've gone wrong. :s-smilie:
Reply 1
Looks like you're correct to me, and Wolfram Alpha agrees. I guess the answer you're asked to prove must be wrong.
Reply 2
TheNack
Looks like you're correct to me, and Wolfram Alpha agrees. I guess the answer you're asked to prove must be wrong.


But it's from the January 2007 Edexcel paper...
_lynx_
I have to show that

f(x) = ln (4x-2)

can be defined as

f^-1(x) = 2 - (1/2)e^x

First of all, I started by swapping x and y around and then rearranged the equation.

y=ln(4x-2)

x=ln(4y-2)

e^x= 4y-2

e^x +2 =4y

(e^x+2)/4=y

I'm not sure where I've gone wrong. :s-smilie:


I just checked the paper, you posted the wrong f(x)
It's ln (4-2x)
Reply 4
Superman_Jr
I just checked the paper, you posted the wrong f(x)
It's ln (4-2x)


The past paper that I was given definitely says ln (4x-2). Thanks for posting the correct form, as I would have been pondering for another hour :rolleyes:

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