Question

Help asap will give brainliest!!!!

Answer 1

Answer:

C

Step-by-step explanation:

ley y = f(x) and rearrange making x the subject

y = $\frac{1}{x+5}$ - 1 ( add 1 to both sides )

y + 1 = $\frac{1}{x+5}$ ( 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 = $\frac{1}{y+1}$ ( subtract 5 from both sides )

x = $\frac{1}{y+1}$ - 5

Change y back into terms of x with x = $f^{-1}$ (x) , then

$f^{-1}$ (x) = $\frac{1}{x+1}$ - 5 where x ≠ - 1