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OpenStudy (rain):

hi can someone help me with this problem, Assume the function has an inverse. Without solving for the inverse find the indicated function values: f(x)=x^3+4x-1, (a) f^-1 (-1) (b) f^-1 (4)

jimthompson5910 (jim_thompson5910):

Let \[\large f^{-1}(-1)=z\] Now apply the function f(x) to both sides to get \[\large -1 = f(z)\] So what this means is that you're looking for an x value that produces a function value of -1. In other words, to find f^{-1}(-1), just plug in f(x)=-1 and solve for x

OpenStudy (zarkon):

f(0)=-1

OpenStudy (zarkon):

f(1)=4

OpenStudy (rain):

Thanks for your responses folks...I really appreciate it. @ Jim, if I do f(-1) wont I just be finding f(x)?

OpenStudy (rain):

@ Zarkon how did you come about f(0) and f(1)?

OpenStudy (zarkon):

I tried simple numbers...when they ask you to find the inverse for specific values without finding the actual inverse function usually the numbers are simple ...like -1,0,1 ;)

jimthompson5910 (jim_thompson5910):

No, not f(-1), you're solving f(x)=-1 for x

OpenStudy (rain):

hmmm.....good point when I do that it comes down to x(x^2+4x)=0...so I know X=0...(good going Zarkon!!! :) ) then I'm left with (x^2+4)=0.....if I factorise this I get (x+2)(x+2)=0...... but when I expand it again I get x^2+4x+4=0......:(

jimthompson5910 (jim_thompson5910):

you cannot factor x^2+4 Notice that (x+2)(x+2) = x^2+2x+2x+4 = x^2+4x+4

OpenStudy (rain):

yes that is what I got

OpenStudy (rain):

so what do I do about that part?

jimthompson5910 (jim_thompson5910):

simply set it equal to zero and solve: x^2+4=0 x^2=-4 x=2i or x=-2i

OpenStudy (rain):

oh....*blush* I should have known that.....I guess sometimes I think its complicated when its not!... :) thank you so much!

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