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any help you all can give me I would appeciate it.
refer to tables as value to find g-1(f-1)(1)
tables x f(x) x g(x)
1 4 1 3
2 3 2 5
3 5 3 2
4 2 4 1
5 1 5 4
answers a.1, b.2, c.3, d.4, e.5
2nd problem
if f(x)=2x2 then f(xth)-f(x)=
4x-1 (x+h)-x
answers a. 4x+4
2h
b. 2h2-4x+1
h
c. 4xh+2h2+8x-2
d. 2x+4
e. 2
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Can anyone tell me what this type of algebra this is?
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The first one seems to be discrete math, or more specifically, set theory. The second one has a hint of calculus. It's pretty much the same as finding a limit.
g-1(f-1)(1)
Do you mean "g inverse composed with f inverse of 1"? Or mathimatically, g-¹(f-¹(1))?
If so, f-¹(1) = 5, and g-¹(5) = 2, so g-¹(f-¹(1)) = 2.
2.
f(x) = 2x - 2, f(x + h) = 2(x + h) - 2
f(x + h) - f(x) = 2x + 2h - 2 - (2x - 2) = 2h.
Now, I believe what you are trying to find is:
(f(x+h) - f(x)) / h
in which case its: 2h / h = 2.
"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."
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