What is the symbolic representation of g^-1(x)?

Question

Find the symbolic representation of g^-1(x).

 

f(x)=(x-5)^2+3

Answer 1

f(x)=(x-5)^2+3

 

Are you looking for the inverse of f(x)?

As in   g(x) = f^-1(x)

 

To find the inverse of a function...

1) replace f(x) with y

y = (x-5)² + 3

 

2) switch y and x in the equation

x = (y-5)² + 3

 

3)  Solve for y

(y-5)² = x - 3

y - 5 =  ±√(x-3)

y = 5 ±√(x-3)

 

4) replace y with f^-1(x)

f^-1(x) = 5 ±√(x-3)

 

Given the duality of the square root, f^-1(x) is not a function because

to be a function every input value, x, in the domain can have one and only one

output value y in the range.