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Question Number 189054 Answers: 1 Comments: 0

Question Number 189053 Answers: 3 Comments: 0

find f(x) 1:f(((x+1)/(x−1)))=x+3; x≠1 2:f(((2x+1)/(x−1)))=x^2 +2x ;x≠1 3:f(x+1)+f(x−y)=2f(x)cosy ∀x,y f(0)=f((π/2))=1

$${find}\:{f}\left({x}\right) \\ $$$$\mathrm{1}:{f}\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}+\mathrm{3};\:{x}\neq\mathrm{1} \\ $$$$\mathrm{2}:{f}\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}\:;{x}\neq\mathrm{1} \\ $$$$\mathrm{3}:{f}\left({x}+\mathrm{1}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){cosy}\:\forall{x},{y} \\ $$$${f}\left(\mathrm{0}\right)={f}\left(\frac{\pi}{\mathrm{2}}\right)=\mathrm{1} \\ $$

Question Number 189049 Answers: 1 Comments: 2

Question Number 189026 Answers: 3 Comments: 0

Question Number 189025 Answers: 0 Comments: 0

Question Number 189024 Answers: 0 Comments: 0

Question Number 189023 Answers: 0 Comments: 3

Question Number 189022 Answers: 3 Comments: 0

if ((√(1+x^2 ))+x)((√(1+y^2 ))+y)=1 with x,y ∈R, find (x+y)^2 =?

$${if}\:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+{x}\right)\left(\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }+{y}\right)=\mathrm{1}\: \\ $$$${with}\:{x},{y}\:\in{R},\:{find}\:\left({x}+{y}\right)^{\mathrm{2}} =? \\ $$

Question Number 189021 Answers: 2 Comments: 4

How many non−similar triangles have integer angles in °?

$${How}\:{many}\:{non}−{similar}\:{triangles} \\ $$$${have}\:{integer}\:{angles}\:{in}\:°? \\ $$

Question Number 189013 Answers: 2 Comments: 0

Suppose (G, ∙ ) and (H, ∗ ) are groups. Take homomorphism φ : G → H. Suppose ∃g∈G : ∣g∣ = n, then ∣φ(g)∣ ≤ n. Does ∀g∈G, ∣g∣ = ∣φ(g)∣ ⇒ G ≅ H ?

$$\mathrm{Suppose}\:\left({G},\:\centerdot\:\right)\:\mathrm{and}\:\left({H},\:\ast\:\right)\:\mathrm{are}\:\mathrm{groups}. \\ $$$$\mathrm{Take}\:\mathrm{homomorphism}\:\phi\::\:{G}\:\rightarrow\:{H}. \\ $$$$\mathrm{Suppose}\:\exists{g}\in{G}\::\:\mid{g}\mid\:=\:{n},\:\mathrm{then}\:\mid\phi\left({g}\right)\mid\:\leqslant\:{n}. \\ $$$$\: \\ $$$$\mathrm{Does}\:\forall{g}\in{G},\:\mid{g}\mid\:=\:\mid\phi\left({g}\right)\mid\:\Rightarrow\:{G}\:\cong\:{H}\:? \\ $$

Question Number 189012 Answers: 0 Comments: 0

Triangle ABC have: sin2A+sin2B+sin2C=(√3)(cosA+cosB+cosC) => Prove that ABC is equilateral triangle

$${Triangle}\:{ABC}\:{have}:\: \\ $$$${sin}\mathrm{2}{A}+{sin}\mathrm{2}{B}+{sin}\mathrm{2}{C}=\sqrt{\mathrm{3}}\left({cosA}+{cosB}+{cosC}\right) \\ $$$$=>\:{Prove}\:{that}\:{ABC}\:{is}\:{equilateral}\:{triangle} \\ $$

Question Number 189000 Answers: 1 Comments: 0

Question Number 188998 Answers: 2 Comments: 3

Question Number 188985 Answers: 1 Comments: 1

Lim_(x→∼) ((4x^3 −2x^2 −5x+4)/(9x^3 −4x^2 +9)) = ??

$$ \\ $$$$\:\:\:\boldsymbol{\mathrm{Lim}}_{\boldsymbol{{x}}\rightarrow\sim} \:\:\frac{\mathrm{4}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{{x}}+\mathrm{4}}{\mathrm{9}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{9}}\:=\:??\: \\ $$

Question Number 188984 Answers: 1 Comments: 4

Lim_(x→∼) (√(16x^2 −2x−1))−4x−5 = ??

$$ \\ $$$$\:\:\boldsymbol{\mathrm{Lim}}_{\boldsymbol{{x}}\rightarrow\sim} \:\sqrt{\mathrm{16}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}−\mathrm{1}}−\mathrm{4}\boldsymbol{{x}}−\mathrm{5}\:=\:??\:\:\:\: \\ $$$$ \\ $$

Question Number 188982 Answers: 0 Comments: 2

Question Number 188981 Answers: 1 Comments: 0

Question Number 188980 Answers: 1 Comments: 0

Question Number 189091 Answers: 1 Comments: 0

1 : Ω = Σ_(n=1) ^∞ (( (− 1 )^( n) H_( n) )/n^( 2) ) = ? 2 : η (−1 )= ?

$$ \\ $$$$\:\:\:\:\mathrm{1}\::\:\:\:\:\Omega\:=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\:\mathrm{1}\:\right)^{\:{n}} \mathrm{H}_{\:{n}} }{{n}^{\:\mathrm{2}} }\:=\:? \\ $$$$\:\:\:\:\mathrm{2}\::\:\:\:\:\:\eta\:\left(−\mathrm{1}\:\right)=\:? \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 189090 Answers: 2 Comments: 0

Question Number 188972 Answers: 0 Comments: 4

what is the answer A ? B ? C?.

$${what}\:{is}\:{the}\:{answer} \\ $$$${A}\:\:?\:{B}\:\:\:?\:{C}?. \\ $$

Question Number 188970 Answers: 1 Comments: 0

LCM(x, 144, 150) = 10800 how many value of x.

$$\mathrm{LCM}\left({x},\:\mathrm{144},\:\mathrm{150}\right)\:=\:\mathrm{10800}\:{how}\:{many}\:{value}\:{of}\:\:{x}. \\ $$$$ \\ $$

Question Number 188968 Answers: 1 Comments: 0

Question Number 188966 Answers: 0 Comments: 0

hey everyone i changed accounts my new one is gatocomcirrose i will not use this one anymore

$$ \\ $$$$\mathrm{hey}\:\mathrm{everyone}\:\mathrm{i}\:\mathrm{changed}\:\mathrm{accounts} \\ $$$$\mathrm{my}\:\mathrm{new}\:\mathrm{one}\:\mathrm{is}\:\mathrm{gatocomcirrose} \\ $$$$\mathrm{i}\:\mathrm{will}\:\mathrm{not}\:\mathrm{use}\:\mathrm{this}\:\mathrm{one}\:\mathrm{anymore} \\ $$

Question Number 188965 Answers: 2 Comments: 0

Question Number 188954 Answers: 0 Comments: 1

Solve : sin(x) + x^2 + tan(x) = 3x Hey!

$$\mathrm{Solve}\:: \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:+\:\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{tan}\left(\mathrm{x}\right)\:=\:\mathrm{3x} \\ $$$$ \\ $$$$\mathrm{Hey}! \\ $$

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