Let f(x)=(x+3)/7. show that f^-1=7x-3. show work.
would the answer just be the inverse steps?

Question

Let f(x)=(x+3)/7. show that f^-1=7x-3. show work.
would the answer just be the inverse steps?

anonymous · Answer

f(x)=y     interchange x and y   solve for y   replace y with f^-1(x)

freckles · Answer

Solve y=(x+3)/7 for x

freckles · Answer

or you know nevermind
we are trying to prove

freckles · Answer

check to see if this is true:
$$f(f^{-1}(x))=f^{-1}(f(x))$$

freckles · Answer

=x

freckles · Answer

$$f(f^{-1}(x))=f^{-1}(f(x))=x$$

anonymous · Answer

sorry i should of put the question

for the function f use composition of functions to show the f^-1 is as given. You may use composition of fuctions or you may find a formula for the inverse.

freckles · Answer

compositions is what i have above

freckles · Answer

f^-1 is 7x-3
so to find f(f^-1(x))
replace first f^-1 with 7x-3
f(7x-3)
replace the x in f with 7x-3

freckles · Answer

and you get x back then you win! :)

freckles · Answer

$$f(f^{-1}(x))=f(7x-3)=$$you need to show this is x

anonymous · Answer

where does the 7x-3 go in the f^-1(x)?

freckles · Answer

f^{-1} is 7x-3
so i just replace f^(-1) with 7x-3

freckles · Answer

you need to plug 7x-3 into f now where x is

freckles · Answer

|dw:1411705970966:dw|