Question

Inverse functions

Answer 1

If \[f(x) = x^5+x^3+x \], find

Answer 2

\[f ^{-1}(3) \] and \[f(f ^{-1}(2))\]

Answer 3

you may find \(f^{-1}(3)\) by inspection,

Answer 4

we ask this q :- wat value of x produces 3 in f(x) ?

Answer 5

1

Answer 6

thats it, we're done.

for the next one il give a hint may be :- \(f\) and \(f^{-1}\) cancel out

Answer 7

Wait so for f^-1 (3) the answer is just 1 then? O_O

Answer 8

yup !

\(x=1\) gives u \(3\) in \(f(x)\)
so \(x=3\) gives u back \(1\) in \(f^{-1}(x)\)

Answer 9

I thought I had to use this formula \[(f ^{-1})'(a) = \frac{ 1 }{ f'(f ^{-1(} }\]

Answer 10

1/f'(f-1(a))

Answer 11

oh you wanto find derivative of \(f^{-1}\) ?

Answer 12

ah no nvm that's for a different question, but so now how do you solve the f(f^-1(2))?

Answer 13

i gave the hint already, thats more than enough for u :)

Answer 14

Oh ahah so the answer is just 2 then ^.^

Answer 15

yes :)

Answer 16

Thanks :P