Hey, we got this sheet for homework. I understand table 1, it's just entered into the calculator, and I understand the above too.
But I just don't understand the last two tables. What's the point of this f-1(x)? What should I interpret from it?
How do I get the solutions, I know that the last table is wrong
(1 votes)
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Hello,
f^(-1)(x) refers to the reversing function, i.e. the function which sputters the associated x value to a given y value.
To find them, you swap y and x of the original function and dissolve after y.
y^2^x.
x and y interchange: x=2^y.
Dissolve after y: ln(x)=y*ln(2).
y=ln(x)/ln(2).
Best regards,
Willy
f-1 means the reverse function and in the end effect you need to swap in the table above only x and y values and get the table for f-1
By the way: In this task it is very clear that in school mathematics it is not a good idea to write fractures as decimal numbers (e.g. 0.125 instead of 1/8). This, in my opinion, completely conceals the connection here.
Sketch for this (The red graph, mirrored at the angle halving, is the graph to reverse function f-1)