Answer:
C
Step-by-step explanation:
ley y = f(x) and rearrange making x the subject
y = [tex]\frac{1}{x+5}[/tex] - 1 ( add 1 to both sides )
y + 1 = [tex]\frac{1}{x+5}[/tex] ( multiply both sides by (x + 5)
(y + 1)(x + 5) = 1 ← expand factors using FOIL
xy + 5y + x + 5 = 1 , that is
xy + x + 5y + 5 = 1 ( factor first/second and third/fourth terms on left side )
x(y + 1) + 5(y + 1) = 1 ← factor out (y + 1) from each term on left side
(y + 1)(x + 5) = 1 ( divide both sides by (y + 1) )
x + 5 = [tex]\frac{1}{y+1}[/tex] ( subtract 5 from both sides )
x = [tex]\frac{1}{y+1}[/tex] - 5
Change y back into terms of x with x = [tex]f^{-1}[/tex] (x) , then
[tex]f^{-1}[/tex] (x) = [tex]\frac{1}{x+1}[/tex] - 5 where x ≠ - 1
