Question

F(x) = (1/x-1) , x>1 , a=2
a- Show that f is one-to-one.
b- Find (f^-1)’(a).
c- Calculate (f^-1)(x) and state the domain and range of (f^-1).
d- Calculate (f^-1)’(a) from the formula in part (c) and check that it agrees with the result of part (b).
e- Sketch the graphs of f and (f^-1) on the same axes.

plzz help me !

Answer 1

a) f(x1)=f(x2) => x1=x2 is basically the definition for one-to-one function (mind you both x1 and x2 should be in domain)...

1/(x1-1) = 1/(x2-1) => x1=x2... hence, it is one-to-one...

Answer 2

ok

Answer 3

b) as our function's Range is (0,inf) we see that it is onto as well...
so, inverse exists...
f(x)=y => f^-1(y) =x -----> (1)

1/(x-1) = y => x= (1/y)+1 ----> (2)

from (1) and (2) => f^-1(y) = (1/y)+1...
f^-1(2) = 1.5 ...

Answer 4

srry, my mistake... thts ur answer for part (c)

Answer 5

its ok

Answer 6

i dont understand the part (b) but everything else can be found from answer to part (c) ... is that enough ??

Answer 7

amm what about part d
its like part c ?

Answer 8

is it*

Answer 9

now that u have got the function find its derivative... using standard rules

Answer 10

aha ok

Answer 11

thanks