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

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) (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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Replace f(x) with y

Swap x and y. Now we isolate y

Subtract 3 from both sides

Divide both sides by 2

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So if the original function is , 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".
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