What is the inverse of f(x)=3/x+1?
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))
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)
To find the inverse of a function, we need to interchange the roles of x and y, and then solve for y. Let's start with the original function f(x) = 3/(x+1):
1. Write the function in the form y = f(x):
y = 3/(x + 1)
2. Swap x and y:
x = 3/(y + 1)
3. Solve for y:
Multiply both sides by (y + 1):
x(y + 1) = 3
Distribute:
xy + x = 3
Subtract x from both sides:
xy = 3 - x
Divide both sides by x:
y = (3 - x)/x
Therefore, the inverse function is f^(-1)(x) = (3 - x)/x.