Suppose f is one-to-one, f(7) = 8, and f'(7) = 8. Find a) f^-1(3) and b) f^-1'(3). I'm kinda stuck on how to find part b). Also check my work for part a) ?

Question

anonymous · Answer

does this problem come with a graph?

jennychan12 · Answer

y-8 = 8(x-7)
y = 8x+48
so f^-1(x) = x = 8y - 48
so x = 8y - 48
so 8y = x+48
so y = (x+48)/8
so f^-1(3) = 51/8 = 6.375

jennychan12 · Answer

no.

anonymous · Answer

ok you found $$y=\frac{ x+48 }{ 8 }$$ for the inverse function right? do you know how to take the derivatives yet?

jennychan12 · Answer

yeah. -_-
OMG. it's that easy...
my teacher showed us a TOTALLY confusing way to do it. 
so i guess i just got too confused. 
so i think i just answered my own question. how sad. :(

anonymous · Answer

haha it's ok :) glad you figured out how to do it!

jennychan12 · Answer

is there a way to do this without finding the inverse function?

anonymous · Answer

yes

jennychan12 · Answer

would you just take the derivative of the original function and flip it? and that would be the derivative of the inverse? idk just a guess.

anonymous · Answer

but i have a question
how do you know the function is a line?

anonymous · Answer

it doesn't say anything about it being a line
if it was a line, they would say 
$f'(x)=8$ not $f'(7)=8$

jennychan12 · Answer

lol i don't. i just assumed. 
ohhhhh now i see it.

anonymous · Answer

in fact there must be some other part missing in the question
knowing that $f(8)=7$ and that $f'(8)=7$ tells you nothing about this function at 3 or its inverse at 3

jennychan12 · Answer

it just says find inverse and inverse derivative at 3. that's all that's given; what i typed.

anonymous · Answer

can you take a picture of the problem?

jennychan12 · Answer

lol my teacher got it from a random website and she posted the problem on her website. and i just copy and pasted whatever she had. THERE IS NO GRAPH.  Suppose f is one-to-one, 
$$f(7) = 8$$
$$f'(7) = 8$$
Find a)
$$f^{-1}(3) $$
b) $$f'^{-1}(3)$$
I just wrote it in a better format. 
i took a picture anyways. it's uploading.

anonymous · Answer

what if she was just trolling you when the real answer would be "cannot conclude answer without enough information"

jennychan12 · Answer

ignore my work and other stuff stuff. it's #2.

anonymous · Answer

i feel like she copied the problem wrong. i don't know any way to acquire this without assuming the equation was linear :( sorry