SOLUTION: Can I please have your assistance? Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x ("multiply by 2, then add 3") to what f -1 does to

Algebra ->  Real-numbers -> SOLUTION: Can I please have your assistance? Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x ("multiply by 2, then add 3") to what f -1 does to      Log On


   

Question 1040341: Can I please have your assistance? Consider f(x) = 2x + 3. Find the inverse of this function. Verbally, compare what f does to x ("multiply by 2, then add 3") to what f -1 does to x.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
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%28x%29+=+2x%2B3


y+=+2x%2B3 Replace f(x) with y


x+=+2y%2B3 Swap x and y. Now we isolate y


x-3+=+2y%2B3-3 Subtract 3 from both sides


x-3+=+2y%2B0


x-3+=+2y


2y+=+x-3


%282y%29%2F2+=+%28x-3%29%2F2 Divide both sides by 2


y+=+%28x-3%29%2F2


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So if the original function is f%28x%29+=+2x%2B3, then the inverse is


Side note: the notation 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 : 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".