# Math

Can you help me with this problem

Find the inverses of each of the functions below algebraically.

a.p(r)=2r2+2r−1

b.3y+5x=18

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1. p = 2r^2+2r-1
swap variables
r = 2p^2+2p-1
2p^2+2p-(1+r) = 0
p = [-2 +/- sqrt(4+8(1+r))]/4
= [-2 +/- sqrt(8r+12)]/4
= [-1 +/- sqrt(2r+3)]/2

So, what's with the 2 values? The original function fails the horizontal-line test, so it has no single inverse. However, if the domain is restricted to a single branch of the parabola (the vertex is at r = -1/2) then the inverse is one of the two values calculated.

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