To find the inverse of a function there are 2 steps:
I'm going to assume that the function is "f(x) = 4 + \\sqrt{x-2}" where the "x-2" is under the radical sign
So the first step is to swap the "f(x)" and "x" . The new function would be
"x = 4 + \\sqrt{f(x) -2}"
Now we'll solve for "f(x)" in the new function
"x = 4 + \\sqrt{f(x) -2}\\\\\n\nx-4 = \\sqrt{f(x) -2}\\\\\n\n(x-4)^2 = f(x) -2\\\\\n\nx^2 - 8x + 16 = f(x) -2\\\\\n\nx^2 - 8x + 18 = f(x)"
So the inverse function, which we write as "f^{-1}(x)" is
Domain of "f(x)"
Range of "f(x)"
"[4, \\infin)"
From the graph, the points "(11, 7)" and "(7, 11)" reflected about point "(9,9)".
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You are well done. I have found the solution to the question so, suitable and accurate. It is good job. Thanks for educational support. More grace to your elbow. Regards Daniel
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