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.
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