Find a symbolic Representation for f ^-1(x)

Question

Find a symbolic Representation for f ^-1(x) 

 

         √¯¯¯¯

f(x) =  x + 8

Answer 1

y = f(x) = √(x+8)

 

Domain: x+8 ≥ 0, x ≥ -8

Range: y ≥ 0

 

Swapping x and y to find inverse:

 

x = √(y+8)

 

Range: y ≥ -8

Domain: x ≥ 0

 

Solve for y:

 

x^2 = y + 8

 

y = f^-1(x) = x^2 - 8, x ≥ 0

 

So the inverse of f(x) = √(x+8) is the right half of the parabola x^2-8.

Answer 2

Keith,

       The inverse f^-1 (x) is the function such that f(f^-1(x)) = x so f^-1 (x)= x² - 8. To find let y=√(x=8) solve for x, x=y² - 8 and replace y with x. 

 

Jim