Question

If f(x) = 9x + 1, find f^–1 (f (3)).

Answer 1

f(x) is a linear function

so it is one-to-one throughout its entire domain

Answer 2

this means that

\[\large f^{-1}(f(x)) = x\]

is true for all values of x

Answer 3

So how would i solve it?

Answer 4

FInd inverse of y=9x+1 once you do then plug in 3. You know how to do inverse?

Answer 5

example:

plug in x = 17 into the function to get some output f(17)

you then plug the output f(17) into the inverse function and you'll get back 17 as the final result

Answer 6

y=9x+1 swap y and x then solve for y :D
x=9y+1 1st step of swapping

Answer 7

so

\[\large f^{-1}(f(17)) = 17\]

Answer 8

yeah i know how to do the inverse (:

Answer 9

but what do i do after i find the inverse?

Answer 10

what did you get for the inverse

Answer 11

y= x+1 over 9.... and then i plug in 3?

Answer 12

after finding inverse plug in your f(3)

Answer 13

it should be

\[\large f^{-1}(x) = \frac{x-1}{9}\]

Answer 14

what you do is plug in x = 3 into f(x) first

once you get your answer, you plug that result into the inverse function and evaluate

Answer 15

oh oops thats what i meant (:

Answer 16

Ohhhhhh okay got it thanks (:

Answer 17

yw

Answer 18

so 3 is what i got is that right?

Answer 19

3 is correct,

if you looked back at my example, I got

\[\large f^{-1}(f(17)) = 17\]

and it turns out that

\[\large f^{-1}(f(x)) = x\]

is true for all x (so just replace x with 3 and you're done)

this works out because f(x) is a linear function

Answer 20

ohhh so I can do that will all of them?

Answer 21

yeah if you know f(x) is a linear function, then \[\large f^{-1}(f(x)) = x\] can be used

Answer 22

okay thanks (:

Answer 23

you're welcome