F(x) = 3x - 12, what is (2)?
2 answers:
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If f(X)= 7x +5/3 - x =6x +5/3
y= 6x +5/3
6x= y-5/3
f^-1(y)=x=(y-5/3)/6
So we can write
f(f^-1(y))= f((y-5/3)/6) = 6 (y-5/3)/6 +5/3= y-5/3+5/3= y
The same result can be obtained for f^-1(f(x))=x
If the function is f(x)= 7x +5/(3-x) then it is not invertible since it is not injective (pictures)
Remark
The idea here is to take any two successive terms and divide one by the other. which is the divisor and which the dividend will be discussed below.
Step One
Set up the ratio for the common ratio between terms that come one after another.
Mathematically this is written as
r =
So just to see how this looks
t_(n + 1) = 3
t_n = 9
r =
r = 1/3
Does this work for other examples? Let's try a more complicated looking one.
t_(n) = 1/9
t_(n+1) = 1/27
r = t_(n + 1) / t_n
r =
r =
r = 1/3
The idea here is to take any two successive terms and divide one by the other. which is the divisor and which the dividend will be discussed below.
Step One
Set up the ratio for the common ratio between terms that come one after another.
Mathematically this is written as
r =
So just to see how this looks
t_(n + 1) = 3
t_n = 9
r =
r = 1/3
Does this work for other examples? Let's try a more complicated looking one.
t_(n) = 1/9
t_(n+1) = 1/27
r = t_(n + 1) / t_n
r =
r =
r = 1/3