Question

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)

Answer 1

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

Answer 2

f(0)=-1

Answer 3

f(1)=4

Answer 4

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

Answer 5

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

Answer 6

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 ;)

Answer 7

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

Answer 8

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......:(

Answer 9

you cannot factor x^2+4

Notice that (x+2)(x+2) = x^2+2x+2x+4 = x^2+4x+4

Answer 10

yes that is what I got

Answer 11

so what do I do about that part?

Answer 12

simply set it equal to zero and solve:

x^2+4=0

x^2=-4

x=2i or x=-2i

Answer 13

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