If f(x)= ln(x^2)-4, give f^-1(x)

For this question we would start by making f(x)=y. As we know the laws of logs, we can say that ln(x2)=2ln(x), therefore our equation can now be written as y= 2ln(x) - 4 . From this point, we want to make x the subject of the equation. We should take the 4 across, making y+4= 2ln(x), and then divide the equation by 2 on both sides to cancel the 2 infront of the 2ln(x). When this is done our equation looks like this: (y+4)/2 =ln(x). To put x on its own, we then have to put both sides as a power of e. As eln(x) cancels to x, we now have the equation x = e(y+4)/2. We can now swap the x position for the y position and our equation becomes f-1(x) = e(x+4)/2

ZT
Answered by Zach T. Physics tutor

2248 Views

See similar Physics A Level tutors

Related Physics A Level answers

All answers ▸

Can you talk me through how to solve problems on projectiles? I always get confused


How would we calculate the distance covered by a train that starts at rest, then accelerates to 5km/hr in 30 mins then stays at this constant speed for 12 minutes?


In a particle accelerator, you accelerate an electron. Afterwards, you measure it's energy to be 350 keV. Tell my why you can't find the speed from this energy using your knowledge of classical mechanics.


A linear accelerator (LINAC) is used to accelerate protons at CERN before they are injected into the Large Hadron Collider. Explain with the aid of a diagram how the proton is accelerated by the LINAC.


We're here to help

contact us iconContact ustelephone icon+44 (0) 203 773 6020
Facebook logoInstagram logoLinkedIn logo

© MyTutorWeb Ltd 2013–2025

Terms & Conditions|Privacy Policy
Cookie Preferences