Hello guys, please help me this one

f(x)= -x^7 - 3x^3 - t + 5 ,
find (f^(-1))'(0)

Thanks

Question

Hello guys, please help me this one

f(x)= -x^7 - 3x^3 - t + 5 , 
find (f^(-1))'(0)

Thanks

anonymous · Answer

Im confused what are you asking whats the" ' " after the brackets mean and why is f^(-1) ? do you mean f(-1) sorry maybe I am of no help here.

precal · Answer

" ' " denotes derivative, this is a calculus question

anonymous · Answer

yep, " ' " means derivative

anonymous · Answer

oh I see you what does the zero in brackets mean?

anonymous · Answer

and what does f^(-1) I might be able to help if understand what you are asking

precal · Answer

slope at that point, if you are studying calculus this is standard notation. 
f^(-1)  inverse function

myininaya · Answer

$$(f^{-1})'(a)=\frac{1}{f'(f^{-1}(a))}$$

anonymous · Answer

I'm not bad at it I just thought inverse was f(x)^-1

anonymous · Answer

is that s'posed to be a "t" in your equation?

myininaya · Answer

$$f(x)=-x^7-3x^3-x+5$$
We need to find $$f^{-1}(0)$$
So what can we plug in that will give us 0?

anonymous · Answer

Wait are we supposed to take the derivative of the inverse and then solve for zero? is that the question?

precal · Answer

yes, but you meant evaluate at zero

anonymous · Answer

lol yeah my bad

precal · Answer

That is ok.  Many problems are posted incorrectly.  People write solve instead of evaluate.  Some people incorrectly write the powers eg  3x2  instead of 3x^2..

myininaya · Answer

well 
we want to figure out what we can plug into that polynomial that will give us 0
so if we plug in 1 what do we get ? :)

myininaya · Answer

so therefore what is 
$$f^{-1}(0)=?$$

myininaya · Answer

$$\text{ Since } f(1)=0 \text{ then } f^{-1}(0)=?$$

anonymous · Answer

they got cut off myin..

myininaya · Answer

what?

myininaya · Answer

Oh you mean the user who asked the question isn't here anymore? :(

anonymous · Answer

you were cut off too for a little while...

anonymous · Answer

keep going please I am interested

myininaya · Answer

What is f inverse of 0 then ?

anonymous · Answer

1

myininaya · Answer

ok$$(f^{-1})'(0)=\frac{1}{f'(f^{-1}(0))}=\frac{1}{f'(1)}$$
The last thing to do is find f'(x)
Then plug in 1 for x
and voo-lah
or is it
woo-lah
?

myininaya · Answer

and put 1 on top of that of course :)

myininaya · Answer

of the f'(1)

anonymous · Answer

ahh makes perfect sense now