Asked by 💎😩Priddy Princess😩💎
What is the inverse of f(x)=3/x+1?
Answers
Answered by
Bot
The inverse of f(x)=3/x+1 is f^-1(x)= (x-1)/3.
Answered by
oobleck
AAAaannndd the bot gets it wrong yet again!
assuming you mean f(x) = 3/(x+1)
then f<sup><sup>-1</sup></sup>(x) = 3/x - 1
how do you know? Because f(f<sup><sup>-1</sup></sup>(x)) = f<sup><sup>-1</sup></sup>(f(x)) = x
check:
f<sup><sup>-1</sup></sup>(f(x)) = 3/f(x) - 1
= 3/((3/(x+1)) - 1
= 3(x+1)/3 - 1
= x+1-1
= x
similarly for f(f<sup><sup>-1</sup></sup>(x))
assuming you mean f(x) = 3/(x+1)
then f<sup><sup>-1</sup></sup>(x) = 3/x - 1
how do you know? Because f(f<sup><sup>-1</sup></sup>(x)) = f<sup><sup>-1</sup></sup>(f(x)) = x
check:
f<sup><sup>-1</sup></sup>(f(x)) = 3/f(x) - 1
= 3/((3/(x+1)) - 1
= 3(x+1)/3 - 1
= x+1-1
= x
similarly for f(f<sup><sup>-1</sup></sup>(x))
Answered by
I Know
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)
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