Write an equation for the inverse function, and then state the domain and range

Question

Write an equation for the inverse function, and then state the domain and range of k and k-1 k(x)=(x-6)" + 9 for x 6 -1 The formula for the inverse is k (x)- The domain of k is [] (Type your answer in interval notation. Use integers or fractions for any numbers in the expression The range of k is Type your answer in interval notation. Use integers or fractions for any numbers in the expression. The domain of k-1 is Type your answer in interval notation. Use integers or fractions for any numbers in the expression.) The range of k is Type your answer in interval notation. Use integers or fractions for any numbers in the expression.)

Explanation / Answer

k(x) = ( x- 6)^2 + 9 for x <= 6

finding formula for k^-1 (x)

y = (x - 6)^2 + 9

x - 9 = ( y - 6 )^2

sqrt ( x - 9 ) = y - 6

y = sqrt ( x - 9 ) + 6

k^-1 (x) = sqrt ( x - 9 ) + 6

domain of k is ( -infinity , 6 ]

range of k is [ 9 , infinity )

domain of k^-1 is [ 9 , infinity )

range of k^-1 is ( -infinity ,6 ]

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