What is the inverse of f(x)=3/x+1?
3 answers
The inverse of f(x)=3/x+1 is f^-1(x)= (x-1)/3.
AAAaannndd the bot gets it wrong yet again!
assuming you mean f(x) = 3/(x+1)
then f-1(x) = 3/x - 1
how do you know? Because f(f-1(x)) = f-1(f(x)) = x
check:
f-1(f(x)) = 3/f(x) - 1
= 3/((3/(x+1)) - 1
= 3(x+1)/3 - 1
= x+1-1
= x
similarly for f(f-1(x))
assuming you mean f(x) = 3/(x+1)
then f-1(x) = 3/x - 1
how do you know? Because f(f-1(x)) = f-1(f(x)) = x
check:
f-1(f(x)) = 3/f(x) - 1
= 3/((3/(x+1)) - 1
= 3(x+1)/3 - 1
= x+1-1
= x
similarly for f(f-1(x))
Unless it was supposed to be as typed ....
f(x)=3/x+1 or y = 3/x + 1
switcheroo
x = 3/y + 1
xy = 3 + y
xy - y = 3
y(x-1) = 3
y = 3/(x - 1) or f^-1(x) = 3/(x - 1)
f(x)=3/x+1 or y = 3/x + 1
switcheroo
x = 3/y + 1
xy = 3 + y
xy - y = 3
y(x-1) = 3
y = 3/(x - 1) or f^-1(x) = 3/(x - 1)