let f(x)=x+2/x+8. what does f^-1(-4) equal?
if y = (x+2)/(x+8), (notice I assumed you have a typo)
the inverse would be
x = (y+2)/(y+8)
sub in x = -4 and solve for y
(I get f^-1(-4) = -34/5)
yes it is. Thank you very much for your help.
To find the value of f^(-1)(-4), we need to find the input value of f(x) that results in the output of -4.
First, let's replace f(x) with -4 in the equation:
-4 = x + 2/x + 8
To simplify the equation, we'll first multiply through by (x + 8) to get rid of the fraction:
-4(x + 8) = x + 2
Expanding the left side of the equation:
-4x - 32 = x + 2
Next, let's move all the terms with x to one side of the equation and the constant terms to the other side:
-4x - x = 2 + 32
Combining like terms:
-5x = 34
To isolate x, divide both sides of the equation by -5:
x = 34 / -5
Finally, we can simplify the value of x:
x = -6.8
Therefore, f^(-1)(-4) is equal to -6.8.