I've spent three days revising functions, although it wasn't enough at all because I think my sources weren't good enough to allow me to become a master in the field of math. By the way, there are two questions which remain because I couldn't solve them.
- $$f:N^2>>>R$$ $$f(n):\left({1\over n}\right)*f(n+1)$$ $$f(1)=1$$ $$f(7)=?$$
I tried this solution, but I didn't understand the $f(1)=1$ rule
$f(n)=\left({fg(n)\over n}\right)$
$\left({fg(n)\over n}\right)=f(n+1)$
$f(n)*n=fg(n)$
$g(n+1)=n$
$n+1=17$
$n=16$
The answer keys says correct answer is 16! but I think ! is typing mistake,isn't it?
- $$f(x)=\left({2x*f(x-1)\over x+1}\right)$$ $$(1)=1$$ $$f(7)=?$$ the way I tried to solve was:
$fg(x)=f(x-1)$
$f(7)=x-1$ and $x=8$
Then I tried lots of methods. They were all wrong.
Tonight I want to finish this subject. It took me lots of extra hours and kept me behind my schedule. I asked many questions tonight, thank you everyone for your help. My concern is for which method I should use to solve this questions in a minute during my exam. I will write my other examples below to show the type of questions which I had been solving the problem with (they're solved no need to resolve) :x
$f(x)+f(x+1)=2x+4$ find $f\left({1\over2}\right)=\text{?}$
$f(x)+2f\left({1\over x}\right)=2x+4$ find $f(2)=\text{?}$
$f(x)=3x-5$ find $f(2x+1)=?$
$f(-x)=2f(x)+6$ find $f(3)=?$
Would you tell me what my weakness in this topic (functions) is, and how I can conclude the topic effectively?
\left(
and\right)
for parentheses surrounding something multilined. Also, if by*
you mean multiplication, either don't put anything or put\cdot
. $\endgroup$