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Question Number 192080 Answers: 1 Comments: 0

f^(−1) (((x+1)/x))=x^3 f^(−1) (x)+f(8)=?

$${f}^{−\mathrm{1}} \left(\frac{{x}+\mathrm{1}}{{x}}\right)={x}^{\mathrm{3}} \:\: \\ $$$${f}^{−\mathrm{1}} \left({x}\right)+{f}\left(\mathrm{8}\right)=? \\ $$

Question Number 192077 Answers: 1 Comments: 0

Let H be a non−empty subset of a group G, prove that the follow− ing are equivalent 1) H is a subgroup of G 2) for a,b ∈ H, ab^(−1) ∈ H 3) for a,b ∈ ab ∈ H 4) for a ∈ H, a^(−1) ∈ H Hint: prove 1)→2)→3)→4)→1) Help!!!

$$\mathrm{Let}\:\mathrm{H}\:\mathrm{be}\:\mathrm{a}\:\mathrm{non}−\mathrm{empty}\:\mathrm{subset}\:\mathrm{of} \\ $$$$\mathrm{a}\:\mathrm{group}\:\mathrm{G},\:\mathrm{prove}\:\mathrm{that}\:\mathrm{the}\:\mathrm{follow}− \\ $$$$\mathrm{ing}\:\mathrm{are}\:\mathrm{equivalent} \\ $$$$\left.\mathrm{1}\right)\:\mathrm{H}\:\mathrm{is}\:\mathrm{a}\:\mathrm{subgroup}\:\mathrm{of}\:\mathrm{G} \\ $$$$\left.\mathrm{2}\right)\:\mathrm{for}\:\mathrm{a},\mathrm{b}\:\in\:\mathrm{H},\:\mathrm{ab}^{−\mathrm{1}} \:\in\:\mathrm{H} \\ $$$$\left.\mathrm{3}\right)\:\mathrm{for}\:\mathrm{a},\mathrm{b}\:\in\:\mathrm{ab}\:\in\:\mathrm{H} \\ $$$$\left.\mathrm{4}\right)\:\mathrm{for}\:\mathrm{a}\:\in\:\mathrm{H},\:\mathrm{a}^{−\mathrm{1}} \:\in\:\mathrm{H} \\ $$$$ \\ $$$$\left.\mathrm{H}\left.\mathrm{i}\left.\mathrm{n}\left.\mathrm{t}\left.:\:\mathrm{prove}\:\mathrm{1}\right)\rightarrow\mathrm{2}\right)\rightarrow\mathrm{3}\right)\rightarrow\mathrm{4}\right)\rightarrow\mathrm{1}\right) \\ $$$$ \\ $$$$\mathrm{Help}!!! \\ $$

Question Number 192076 Answers: 1 Comments: 0

f(x)=x^2 +6x f^(−1) (x)=?

$${f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{6}{x}\:\:\:\:{f}^{−\mathrm{1}} \left({x}\right)=? \\ $$

Question Number 192073 Answers: 1 Comments: 0

Reponse a l exercice deja pose

$$\mathrm{Reponse}\:\mathrm{a}\:\:\mathrm{l}\:\mathrm{exercice}\:\mathrm{deja}\:\:\mathrm{pose} \\ $$

Question Number 192062 Answers: 2 Comments: 3

prove it : times_n ; (√(4+(√(4+(√(4+...+(√4))))) )) < 3

$${prove}\:{it}\::\: \\ $$$$\:\:\:{times\_n}\:\:\:;\:\:\:\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+\sqrt{\mathrm{4}+...+\sqrt{\mathrm{4}}}}\:\:}\:<\:\mathrm{3} \\ $$

Question Number 192057 Answers: 1 Comments: 0

Simplify: (((√a) + (√a^2 ) + (√a^3 ) + (√a^4 ))/(((√a) + 1)∙(a + 1)))

$$\mathrm{Simplify}: \\ $$$$\frac{\sqrt{\mathrm{a}}\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{2}} }\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{3}} }\:\:+\:\:\sqrt{\mathrm{a}^{\mathrm{4}} }}{\left(\sqrt{\mathrm{a}}\:\:+\:\:\mathrm{1}\right)\centerdot\left(\mathrm{a}\:\:+\:\:\mathrm{1}\right)} \\ $$

Question Number 192054 Answers: 1 Comments: 0

If Q = ((2−x)/(y−1)) ; −5≤x<−1 , 5≤y<6 Find Q_(max) .

$$\:\:\:\mathrm{If}\:\mathrm{Q}\:=\:\frac{\mathrm{2}−\mathrm{x}}{\mathrm{y}−\mathrm{1}}\:;\:−\mathrm{5}\leqslant\mathrm{x}<−\mathrm{1}\:,\:\mathrm{5}\leqslant\mathrm{y}<\mathrm{6} \\ $$$$\:\:\:\mathrm{Find}\:\mathrm{Q}_{\mathrm{max}} .\: \\ $$

Question Number 192049 Answers: 2 Comments: 0

fog(x)=4x−1 g(x)=x−2 f(x)=?

$${fog}\left({x}\right)=\mathrm{4}{x}−\mathrm{1} \\ $$$${g}\left({x}\right)={x}−\mathrm{2} \\ $$$${f}\left({x}\right)=? \\ $$

Question Number 192048 Answers: 1 Comments: 0

if the combined function is h(x)=(√(3x^2 +1)) then find the tow other functions of its.

$${if}\:{the}\:{combined}\:{function}\:{is}\:{h}\left({x}\right)=\sqrt{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{1}} \\ $$$${then}\:{find}\:{the}\:{tow}\:{other}\:{functions}\:{of}\:{its}. \\ $$

Question Number 192047 Answers: 1 Comments: 0

we have three digit number like XYZ that X+Y+Z=16, if we replace X by Z then it will be changed to ZYX number that ZYX=XYZ−594 find XYZ number.

$${we}\:{have}\:{three}\:{digit}\:{number}\:{like}\:{XYZ} \\ $$$${that}\:{X}+{Y}+{Z}=\mathrm{16},\:{if}\:{we}\:{replace}\:{X}\:{by}\:{Z} \\ $$$${then}\:{it}\:{will}\:{be}\:{changed}\:{to}\:{ZYX}\:{number}\: \\ $$$${that}\:{ZYX}={XYZ}−\mathrm{594} \\ $$$${find}\:{XYZ}\:{number}. \\ $$

Question Number 192033 Answers: 2 Comments: 0

Question Number 192044 Answers: 0 Comments: 0

Question Number 192045 Answers: 0 Comments: 0

(1/((1+(√2))(1+(2)^(1/4) )(1+(2)^(1/8) )(1+(2)^(1/(16)) )))×(((1−(2)^(1/(16)) )/(1−(2_ )^(1/(16)) ))) ⇒_ ((1−(2)^(1/(16)) )/((1+(√2))(1+(2)^(1/4) )(1+(2)^(1/8) )(1−(2)^(1/8) )))⇒(1/((1+(√2))(1+(2)^(1/4) )(1−(2)^(1/4) )))

Question Number 192024 Answers: 1 Comments: 0

Question Number 192023 Answers: 2 Comments: 0

Question Number 192046 Answers: 2 Comments: 0

tow type creams are in a box that one type of these have 25gr mass and another ones have 37gr mass, if the total mass of those is 870gr then find the number of each type of creams.

$${tow}\:{type}\:{creams}\:{are}\:{in}\:{a}\:{box}\:{that}\:{one}\: \\ $$$${type}\:{of}\:{these}\:{have}\:\mathrm{25}{gr}\:{mass}\:{and}\:{another} \\ $$$${ones}\:{have}\:\mathrm{37}{gr}\:{mass},\:{if}\:{the}\:{total}\:{mass} \\ $$$${of}\:{those}\:{is}\:\mathrm{870}{gr}\:{then}\:{find}\:{the}\:{number} \\ $$$${of}\:{each}\:{type}\:{of}\:{creams}. \\ $$

Question Number 192039 Answers: 0 Comments: 0

let x,y,z be positive real number such that x^4 +y^4 +z^4 = 1 find the minimum value of (x^3 /(1−x^8 )) + (y^3 /(1−y^8 )) + (z^3 /(1−z^8 ))

$$\mathrm{let}\:{x},{y},{z}\:\mathrm{be}\:\mathrm{positive}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:{x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} \:=\:\mathrm{1}\:\mathrm{find}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\mathrm{of} \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{3}} }{\mathrm{1}−{x}^{\mathrm{8}} }\:+\:\frac{{y}^{\mathrm{3}} }{\mathrm{1}−{y}^{\mathrm{8}} }\:+\:\frac{{z}^{\mathrm{3}} }{\mathrm{1}−{z}^{\mathrm{8}} } \\ $$

Question Number 192015 Answers: 1 Comments: 0

Question Number 192013 Answers: 0 Comments: 0

∫e^(at^b ) dt with a,b as a constant how to evaluate this

$$ \\ $$$$\:\int{e}^{{at}^{{b}} } {dt} \\ $$$$\:{with}\:{a},{b}\:{as}\:{a}\:{constant} \\ $$$$\:{how}\:{to}\:{evaluate}\:{this} \\ $$$$ \\ $$

Question Number 192009 Answers: 2 Comments: 0

if a>1 , show ((Σ_(k=1) ^(a^2 −1) (√(a+(√k))))/(Σ_(k=1) ^(a^2 −1) (√(a−(√k))))) = (√2) + 1

$$\:\:\:\:\:{if}\:\:{a}>\mathrm{1}\:,\:{show} \\ $$$$\:\:\:\:\:\frac{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}+\sqrt{{k}}}}{\underset{{k}=\mathrm{1}} {\overset{{a}^{\mathrm{2}} −\mathrm{1}} {\sum}}\:\:\sqrt{{a}−\sqrt{{k}}}}\:\:\:=\:\:\:\sqrt{\mathrm{2}}\:\:+\:\:\mathrm{1} \\ $$

Question Number 192001 Answers: 2 Comments: 1

Question Number 191997 Answers: 1 Comments: 2

Show that C={−1,1,−ı,ı} where ı=(√(−1)) with addition operation is a group. Help!

$$\mathrm{Show}\:\mathrm{that}\:\mathbb{C}=\left\{−\mathrm{1},\mathrm{1},−\imath,\imath\right\}\:\mathrm{where} \\ $$$$\imath=\sqrt{−\mathrm{1}}\:\mathrm{with}\:\mathrm{addition}\:\mathrm{operation}\:\mathrm{is}\:\mathrm{a} \\ $$$$\mathrm{group}. \\ $$$$ \\ $$$$\mathrm{Help}! \\ $$

Question Number 191993 Answers: 0 Comments: 0

Question Number 191986 Answers: 1 Comments: 0

Ques. 1 Let (G,∗) be a group, then show that for each a∈G, ∃ a unique element e∈G ∣ a∗e=e∗a=a Ques. 2 If a∈G ⇒ x∈G and x is unique show that if x∗a=e, then a∗x=e. Hello!

$$\mathrm{Ques}.\:\mathrm{1} \\ $$$$\mathrm{Let}\:\left(\mathrm{G},\ast\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{group},\:\mathrm{then}\:\mathrm{show} \\ $$$$\mathrm{that}\:\mathrm{for}\:\mathrm{each}\:\mathrm{a}\in\mathrm{G},\:\exists\:\mathrm{a}\:\mathrm{unique}\: \\ $$$$\mathrm{element}\:\mathrm{e}\in\mathrm{G}\:\mid\:\mathrm{a}\ast\mathrm{e}=\mathrm{e}\ast\mathrm{a}=\mathrm{a} \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{2} \\ $$$$\mathrm{If}\:\mathrm{a}\in\mathrm{G}\:\Rightarrow\:\mathrm{x}\in\mathrm{G}\:\mathrm{and}\:\mathrm{x}\:\mathrm{is}\:\mathrm{unique} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{x}\ast\mathrm{a}=\mathrm{e},\:\mathrm{then}\:\mathrm{a}\ast\mathrm{x}=\mathrm{e}. \\ $$$$ \\ $$$$ \\ $$$$\mathrm{Hello}! \\ $$

Question Number 191966 Answers: 1 Comments: 0

Question Number 191962 Answers: 1 Comments: 0

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