Category: Relation and Functions

Question Number 926 by 123456 last updated on 26/Apr/15 $$a(n,m)=\{\begin{array}{ll}m& n⩽0\\ na(n+m-1,m)+m& n>0\vee m⩽0\\ na(n-m,m-1)+m+m^2& n>0\vee m>0\end{array}$$$$a(5,5)=???$$$$a(10,10)=??$$ Commented by 123456 last updated on 27/Apr/15 $${a}\left(\mathrm{0},{m}\right)={m}…

Question Number 874 by 123456 last updated on 08/Apr/15 $$f:\mathbb{R}\to \mathbb{R}$$$$g:\mathbb{R}\to \mathbb{R}$$$$f\left(x\right)=g\left(x\right)-f(-x)$$$$g\left(x\right)=f\left(x\right)+g(-x)$$$$f\left(x\right)=?$$$$g\left(x\right)=?$$$$f\left(x\right)+g\left(x\right)=?$$$$\boldsymbol{{f}}\left(\boldsymbol{{x}}\right)\overset{?} {=}\boldsymbol{{f}}\left(−\boldsymbol{{x}}\right)…

Question Number 830 by prakash jain last updated on 20/Mar/15 $$f\left(x\right)\mathrm{is}\mathrm{a}\mathrm{polynomial}\mathrm{such}\mathrm{that}$$$$f\left(x^2\right)=f\left(x\right)f(x-1)$$$$\mathrm{Find}f\left(x\right)\mathrm{such}\mathrm{that}f\left(x\right)\ne 0.$$ Commented by 123456 last updated on 23/Mar/15…

Question Number 818 by 123456 last updated on 17/Mar/15 $$f:\mathbb{R}\to \mathbb{R}$$$$g:\mathbb{R}\to \mathbb{R}$$$$f\left(xy\right)=f\left(x\right)g\left(x\right)+f\left(y\right)g\left(y\right)$$$$g\left(xy\right)=f\left(x\right)g\left(y\right)+f\left(y\right)g\left(x\right)$$$$\frac{d\left(fg\right)}{dx}=?$$ Commented by prakash jain last…

Question Number 806 by 123456 last updated on 16/Mar/15 $$ifp\left(x\right)isapolynomialand$$$$p\left(x\right)p\left(\frac{1}{x}\right)=p\left(x\right)+p\left(\frac{1}{x}\right)$$$$p\left(3\right)=28$$$$then$$$$p\left(x\right)=?$$$$p\left(4\right)=?$$ Commented by 123456…