Finding linear function

[letsgetaway]

I have two problems. I'm just wondering if I'm on the right track for solving it. On the second problem, I'm not sure where to start, but I did make a guess.


#1. Find the linear fuction f(x) satisfying f(4)=4 and the point (-2, 10) is on the graph of f^-1.

My solution for this problem is...

Find slope using the points (4,4) and (-2,10).  Then use point slope form which will give you the linear function.  Thus, in short form, my answer is...   

y=-x+8

#2. Given that the x and y intercepts of the inverse function are -2 and 6, find the equation for the linear function f(x).

My first guess is that the x and y intercepts should be interchanged from the inverse.

(-2, 6)  to  (6, -2)

That's all I have guessed for trying to figure out the answer.

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[tkhunny]

I didn't check your answers, since you did not give us any clue concerning your methodology.

If f-inverse has points (4,4) and (-2,10), then f(x) has points (4,4) and (10,-2). Do you know why?

Likewise, if f-inverse has points (-2,0) and (0,6), then f(x) has points (0,-2) and (6,0). Do you know why?

Note: This is, in my view, an ingenious problem. I have not ever seen one like it. This always points out to me the fact that mathematics is NOT a course in memorization. Though it is a new problem, the likes of which I never have seen, still, I was able to reason it out and solve it. This does not make it pat-me-on-the-back day, it makes it mathematics-is-cool day!!

 

[letsgetaway]

I didn't check your answers, since you did not give us any clue concerning your methodology.

If f-inverse has points (4,4) and (-2,10), then f(x) has points (4,4) and (10,-2). Do you know why?

Likewise, if f-inverse has points (-2,0) and (0,6), then f(x) has points (0,-2) and (6,0). Do you know why?

Note: This is, in my view, an ingenious problem. I have not ever seen one like it. This always points out to me that fact that mathematics is NOT a course in memorization. Though it is a new problem, the likes of which I never have seen, still, I was able to reason it out and solve it. This does not make it pat-me-on-the-back day, it makes it mathematics-is-cool day!!

Thanks. These were questions from an online quiz. The math department at school makes up these problems. The lesson on linear functions was so brief that the class was only told the formula. I understand your reasoning for getting the points now.