Question 1155728
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The function "f(x) = x+5/2" = {{{f(x) = x+5/2}}} is not very interesting; so I am going to assume that the function is supposed to be "f(x) = (x+5)/2" = {{{f(x) = (x+5)/2}}}<br>
The standard method for finding the inverse of a function is to switch the x and y in the given function and solve for the new y:<br>
Switch:  {{{y = (x+5)/2}}}  -->  {{{x = (y+5)/2}}}<br>
Now solve for y.<br>
{{{x = (y+5)/2}}}
{{{2x = y+5}}}
{{{2x-5 = y}}}
{{{y = 2x-5}}}<br>
ANSWER: f^(-1)(x) = 2x-5<br>
For many simple functions, it is easier to find the inverse by using the fact that the inverse function "gets you back where you started".<br>
To get you back where you started, the inverse function has to performs the opposite operations, in the opposite order, compared to the original function.<br>
The given function does the following to the input value:
(1) add 5;
(2) divide by 2<br>
The inverse function has to...
(1) multiply by 2;
(2) subtract 5<br>
f^(-1)(x) = 2x-5<br>
Same answer with much less work...<br>