Let f(x)=(x+7)/(x+5). inverse f-1(-3)=...
let y = (x+7)/(x+5)
to form the inverse, interchange the x and y variables, thus
x = (y+7)/(y+5)
xy + 5x = y + 7
xy - y = 7 - 5x
y(x-1) = 7-5x
y = (7-5x)/(x-1)
so f-1(x) = (7-5x)/(x-1)
and
f-1(-3) = (7-5(-3))/((-3)-1)
= 22/-4 = -11/2
f-1(-3) = (5-7(-3))/((-3)-1)
= 26/-4 = -13/2
thanks!
nope!
checking :
subbing my answer of -11/2 back in the original function yields -3
Your answer of -13/2 does not.
To find the inverse of a function, we need to solve the equation f(x) = y for x.
Given that f(x) = (x+7)/(x+5), we can rewrite this equation as:
y = (x+7)/(x+5)
Now, let's solve this equation for x.
Step 1: Swap the roles of x and y.
x = (y+7)/(y+5)
Step 2: Solve for y.
Multiply both sides of the equation by (y+5):
x(y+5) = y+7
xy + 5x = y + 7
Move all terms involving y to one side and all the other terms to the other side:
xy - y = 7 - 5x
Factor out y on the left side:
y(x - 1) = 7 - 5x
Now, divide both sides by (x - 1):
y = (7 - 5x)/(x - 1)
Thus, the inverse function f^(-1)(x) is:
f^(-1)(x) = (7 - 5x)/(x - 1)
Now, to find f^(-1)(-3), substitute -3 in place of x:
f^(-1)(-3) = (7 - 5(-3))/((-3) - 1)
f^(-1)(-3) = (7 + 15)/(-4)
f^(-1)(-3) = 22/(-4)
Finally, simplifying the expression:
f^(-1)(-3) = -11/2 or -5.5
Therefore, f^(-1)(-3) is -11/2 or -5.5.