Inverse Help Plz? (1 Viewer)

[starbuckscoffee]

Inverse Help Plz?

1. For f:R---->R, f(x) = 2e^x -4
Find the coordinates of the points of intersection of the graph of y=f(x) and y=f^-1(x)

2. For f:R----->R, f(x)= 2loge (x+3) +4
Find the coordinates of the points of intersection of the graph of y=f(x) and y=f^-1(x)

3. how do you make x the subject in, y=5(1-e^-x)
Thanks

 

[Slidey]

1) y=2e^x-4
The inverse is y=ln(x+4)-ln2
Hmm. You could use Newton's method but that's not exact. Let's try another way:
y=2e^x-4, the inverse is:
x=2e^y-4, thus intersection at:
y=2e^(2e^y-4)-4, hmm
Nah mate I can't think of anything. Guess you need to use Newton's method or graphing.

I mean, obviously the point of intersection is when y=x (or of the form (x,y)=(x,x)) so that means you don't need to worry about the inverse, but it still seems to be a transcendental function to me.
y=ln((y+4)/2), or
x=2e^x-4

Neither seems solvable with algebra.

Similar for 2.

3) y/5=1-e^(-x)
y/5 - 1 = -e^(-x)
ln(1-y/5)=-x
x=-ln(1-y/5)
Thus the inverse is:
y=ln(5)-ln(5-x)