Inverse of a function (Gr 12 math)

[Senjai]

Inverse of a function.. (Gr 12 math) [SOLVED]

Homework Statement

If point (a,b) is on the line of y = f(x), what poin must be on the line of:

1. y = $$f\left(-\frac{1}{2}x\right)+1$$
2. *Trouble question* $$y=f^{-1}(x)+2$$

Homework Equations

The Attempt at a Solution

My answer for the first was : $$\left(-\frac{1}{2}a, b+2\right)$$

the second one bothers me... i know you have to swap the domain and range. but normally the questions i get are if y = 2x + 3, what is the inverse of the function. I then swap the x and y to get x = 2y + 3 then rearrange to end up with the answer y= (x-3)/2 but i don't really know where to start here...

I don't have an answer key for this worksheet. but what do i do, do i just go x = y +2 and do the reverse, then i would answer (a-2, b+2)? This is really bugging me.

Regards,
Senjai

 

[HallsofIvy]

Homework Statement

If point (a,b) is on the line of y = f(x), what poin must be on the line of:

1. y = $$f\left(-\frac{1}{2}x\right)+1$$
2. *Trouble question* $$y=f^{-1}(x)+2$$

Homework Equations

The Attempt at a Solution

My answer for the first was : $$\left(-\frac{1}{2}a, b+2\right)$$

No. You are completely misunderstanding the point of the problem. All you know about f is that f(a)= b so to be able to find f((1/2)x) at all, you must have (1/2)x= a. Now what is x? And, since f((1/2)x)= f(a)= b, what is y?

the second one bothers me... i know you have to swap the domain and range. but normally the questions i get are if y = 2x + 3, what is the inverse of the function. I then swap the x and y to get x = 2y + 3 then rearrange to end up with the answer y= (x-3)/2 but i don't really know where to start here...

I don't have an answer key for this worksheet. but what do i do, do i just go x = y +2 and do the reverse, then i would answer (a-2, b+2)? This is really bugging me.

What happened to f? This has nothing at all to do with "x=y+2" or "y= x=- 2".
Since all you know about f is that f(a)= b, all you know about f^-1 is that f^-1(b)= a. So in order to say anything at all about f^-1(x), you must have x= b. In that case, f^-1(x)= f^-1(b)= a. So what is f^-1(x)+ 2.

Notice that in neither of these questions are you asked anything very general- just to determine a single point on the graph.

Regards,
Senjai