SOLUTION: Find the inverse function using diagrams and test points f(x) = 2x + 1 Select one: a. f ^-1(x) = (x/2) -1 b. f ^-1(x) = (x/2) +1 c. f ^-1(x) = x-1/2 d. f ^-1(x) = x+1/2

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Question 1093683: Find the inverse function using diagrams and test points
f(x) = 2x + 1
Select one:
a. f ^-1(x) = (x/2) -1
b. f ^-1(x) = (x/2) +1
c. f ^-1(x) = x-1/2
d. f ^-1(x) = x+1/2
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source):
You can put this solution on YOUR website!
Your given function appears graphed like .

If you reflect that line through , then the resulting reflection is .
and the purple line is the inverse for your given f(x).

None of your choices match the inverse of f(x).

Answer by greenestamps(13200) (Show Source):
You can put this solution on YOUR website!

An interesting idea -- to find the inverse of a linear function by using test points. If we find two (x,y) values that satisfy the given equation and switch the x and y values in each pair, then we will have two points that satisfy the inverse function. Then using those two points we can find the equation of the linear function that contains both of them.

But that method won't work for anything other than a linear function....

Okay, so two points that lie on the graph of the given function are (0,1) and (1,3).

Switching the coordinates, we get the point (3,1) and (1,0). A quick calculation shows the slope of that line is 1/2; and then using that slope with either point we can find that the equation of the inverse function is

So the first response you got to your question is right -- none of the answer choices is the correct inverse function.