I don't understand how to calculate a function when there is a negative exponent.

Question

If f(x)=x²-4x+4 for x> or =2. What is the formula for f^-1? I don't know how to calculate a negative in that position.

Answer 1

f^-1(x) is inverse function for f(x) 

1. You have to write given function with dependent variable "y" 
2. Then solve the two variable equation for "x"
3. Then switch places for "x" and "y"
~~~~~~~~~~ 

f(x) = x² - 4x + 4 

y = x² - 4x + 4 

y = (x - 2)²   (domain is x ≥ 2, and range is y ≥ 0) 

x - 2 = √y

x = (√y) + 2

y = (√x) + 2

f^-1(x) = (√x) + 2 

Answer 2

If the negative exponent is on a variable, then it is the same as dividing by the number to that power.

 

Example:

 

x^(-2)

 

is the same as

 

    1

----------

  x^(2)