OpenStudy (anonymous):

I do not understand inverse functions exactly so if you could explain this problem that would be great If f(x) = 2x, then f -1(x) =

3 years ago
OpenStudy (anonymous):

the inverse function is a function that acts opposed to the original function in such a way that it gets a value of y and gives you a value of x. However, the original function does it but in a reversed way in which upon introducing an x to its argument it will give you a value of y.

3 years ago
OpenStudy (anonymous):

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3 years ago
OpenStudy (anonymous):

got it?

3 years ago
OpenStudy (anonymous):

so the reverse of 2x would be -2x? right?

3 years ago
OpenStudy (anonymous):

would that be the right answer for that inverse problem

3 years ago
OpenStudy (anonymous):

e.g., consider the simple function f(x)=2x. let's know what f(x) would get for x=2. Substituting x=2 in 2x gives f(2)= 2*2=4. then the inverse is such that it must turn the input value y=4 into out put value x=2. We must look for a candidate that does it for us. If we choose f(x)=1/2x it would get the desired result because f(4)=1/2*4=2

3 years ago
OpenStudy (phi):

f(x) = 2x is a rule. You give it a number and it returns a new number example: we give it 1, and it returns 2 or we give it 10, and it returns 20 the inverse takes the *new number* example, the 20, and returns the original number e.g. the 10

3 years ago
OpenStudy (anonymous):

okay that kind of makes sense

3 years ago
OpenStudy (phi):

if you have f(x) and it returns a number y then f^-1 will take the y and return back the original x the inverse "undoes" the function. we start x --> function --> y --> inverse --> x using formulas, we would write that as \[ f^{-1}(f(x)) = x \] which is a complicated way of saying the inverse undoes the function

3 years ago
OpenStudy (phi):

if you have f(x)= 2x and we put in x=0 we get out 0. (0,0) is the (in, out) pair if we put in 1 we get out 2, (1,2) put in 2, we get 4 (2,4) the inverse would swap those pairs: (0,0), (2,1), (4,2)

3 years ago
OpenStudy (anonymous):

oh okay I get it now thank you

3 years ago
OpenStudy (phi):

the way to find the inverse is use the idea that (x,y) pair for the function becomes (y,x) for the inverse. we relabel f(x)=2x as y= 2x swap y and x: (make y an x and vice versa) to get x= 2y now "solve for y" you start with 2y= x divide both sides by 2: 2y/2 = x/2 on the left 2/2 is 1, and we get y = x/2 or \[ y = \frac{1}{2} x \]

3 years ago
OpenStudy (phi):

and finally, relabel y as f^-1 \[ f^{-1}(x)= \frac{1}{2}x \]

3 years ago