Asked by Tomar
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
Find the inverses of each of the functions below algebraically.
a.p(r)=2r2+2r−1
b.3y+5x=18
Answers
Answered by
Steve
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.
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.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.