Question 1111671
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(1) A formal algebraic process for finding the inverse of a function: switch x and y and solve for the new y:
{{{x = log((y-7))}}}
{{{10^x = y-7}}}
{{{10^x+7 = y}}}<br>
The inverse is {{{y = 10^x+7}}}.<br>
(2) A different way to find an inverse, if the function is relatively simple:<br>
Since an inverse function "un-does" what the function does, determine what operations were performed on the input by the original function; the inverse function will perform the inverse operations in the opposite order.<br>
For this example, the operations performed on the input by the original function are
(1) subtract 7
(2) take log base 10<br>
The inverse operations, in the opposite order, are
(1) raise 10 to the power
(2) add 7<br>
The inverse is {{{y=10^x+7}}}