Mathematical problem 2x / (X-7) plus X-7 / 2x is equal to 2 2 / X-2 plus MX / X squared minus 4 is equal to 3 / x plus 2. Find m with increasing root

Let 2x / (X-7) = a
Then (X-7) / 2x = 1 / A
a+1/a=2
a²+1=2a
a²-2a+1=(a-1)²=0
a=1
2x/(x-7)=1
2x=x-7
x=-7

Given that f (x) = 2x + 1, how to find the analytic formula of F (x-1)? Can X-1 be directly substituted into the formula? Why?

f(x-1)=2(x-1)+1=2x-1
What can be substituted is that the position of X represents the independent variable, while X-1 can be regarded as a whole and can still be regarded as the independent variable, so of course it can be substituted into the calculation

F (2x + 1) = X-9, find the analytic formula of F (x) (to solve the problem in detail)

f(2x+1)=x-9
(1)
Patchwork method:
f(2x+1)=1/2(2x+1)-9-1/2
=1/2(2x+1)-19/2
therefore
f(x)=x/2-19/2
(2)
Let 2x + 1 = t
x=(t-1)/2
f(t)=(t-1)/2-9
=t/2-19/2
therefore
f(x)=x/2-19/2

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