Question 1040341
Here's the basic outline to finding the inverse.



Step 1) Replace f(x) with y



Step 2) Swap x and y



Step 3) Solve for y



Let's follow this outline to find the inverse.



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{{{f(x) = 2x+3}}}



{{{y = 2x+3}}} Replace f(x) with y



{{{x = 2y+3}}} Swap x and y. Now we isolate y



{{{x-3 = 2y+3-3}}} Subtract 3 from both sides



{{{x-3 = 2y+0}}}



{{{x-3 = 2y}}}



{{{2y = x-3}}}



{{{(2y)/2 = (x-3)/2}}} Divide both sides by 2



{{{y = (x-3)/2}}} 



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So if the original function is {{{f(x) = 2x+3}}}, then the inverse is *[Tex \LARGE f^{-1}(x) = \frac{x-3}{2}]



Side note: the notation *[Tex \LARGE f^{-1}(x)] means "inverse of f(x)"



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Now let's compare the verbal descriptions



Original function f(x): multiply the number (x) by 2, then add 3



Inverse function *[Tex \LARGE f^{-1}(x)]: subtract 3 from the number (x), then divide by 2



Essentially whatever you applied to the original function, you follow in reverse undoing the order and applying the opposite operation (eg: the opposite of addition is subtraction). So if you added 3 to the unknown number, then you undo that by subtracting 3 from the number when it comes to the inverse. In a sense, "inverse" means "opposite".