contestada

Consider the function f(x)=[tex]\sqrt{x+2}-6[/tex] for the domain [-2,∞)
Find [tex]f^{-1}(x)[/tex], where [tex]f^{-1}[/tex] is the inverse of [tex]f[/tex].
Also state the domain of [tex]f^{-1}[/tex] in interval notation.

Respuesta :

sqdancefan

Answer:

  • f^-1(x) = (x+6)^2 -2
  • domain: [-6, ∞)

Step-by-step explanation:

To find the inverse function of f(x), we solve for y the equation ...

  x = f(y)

  x = √(y+2) -6

  x +6 = √(y +2)

  (x +6)^2 = y + 2

  (x +6)^2 -2 = y

The inverse function is ...

  [tex]f^{-1}(x)=(x+6)^2-2[/tex]

The domain of f^-1 is the range of the function f(x): [-6, ∞).

Ver imagen sqdancefan

Otras preguntas