Question

For the function f(x)= √x-6 +1, find the inverse function.

Answer 1

f^(-1) (x) = (x-1)²+6 x≥6

Explanation:

y=√(x-6) +1 original for the inverse x and y switch places because you are rflecting the function over the line y=x

y=√(x-6) +1 now the job is solve for y by using inverse operations. Think about undoing the equation.

x-1=√(y-6) subtract 1

(x-1)²=y-6 square both sides of the equation

(x-1)²+6=y add 6 to both sides

x≥6 because we are only using real numbers and if x is less than 6 you get a negative number under the square root sign.