Asked by ALLI

the function f(x)=6x+9/3x-7

find the inverse and check answer

f^-1(x)=?

please show work
Answered by Reiny
I have a strong feeling you meant
f(x) = (6x+9)/(3x-7)

if so, let
y = (6x+9)/(3x-7)
inverse:
x = (6y+9)/(3y-7)

solving that for y ....

3xy - 7x = 6y+9
3xy - 6y = 7x+9
y(3x - 6) = 7x+9
y = (7x+9)/(3x-6)

<b>f^-1 (x) = (7x+9)/(3x-6)</b>

check:
f(0) = 9/-7
f^-1(-9/7) = (7(-9/7) + 9)/(3(-9/7)-6)
= 0/...
= 0

(This does not prove that my answer is correct, but shows a very strong probability that it is correct)
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