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Question-80365




Question Number 80365 by gny last updated on 02/Feb/20
Commented by gny last updated on 02/Feb/20
sir plz help me
$${sir}\:{plz}\:{help}\:{me} \\ $$
Commented by mr W last updated on 02/Feb/20
you sir please help us!!!  how can somebody help you if you don′t  tell him what your question is?
$${you}\:{sir}\:{please}\:{help}\:{us}!!! \\ $$$${how}\:{can}\:{somebody}\:{help}\:{you}\:{if}\:{you}\:{don}'{t} \\ $$$${tell}\:{him}\:{what}\:{your}\:{question}\:{is}? \\ $$
Commented by jagoll last updated on 02/Feb/20
what your request?
$${what}\:{your}\:{request}? \\ $$
Commented by Rio Michael last updated on 02/Feb/20
dude what do we do with   that function??
$$\mathrm{dude}\:\mathrm{what}\:\mathrm{do}\:\mathrm{we}\:\mathrm{do}\:\mathrm{with}\: \\ $$$$\mathrm{that}\:\mathrm{function}?? \\ $$
Commented by gny last updated on 02/Feb/20
find the number of values that (×) can get
$${find}\:{the}\:{number}\:{of}\:{values}\:{that}\:\left(×\right)\:{can}\:{get} \\ $$
Commented by Rio Michael last updated on 02/Feb/20
i don′t understand
$$\mathrm{i}\:\mathrm{don}'\mathrm{t}\:\mathrm{understand} \\ $$
Answered by MJS last updated on 02/Feb/20
f(x)=((x−4)/(2x−6))  defined for x∈R\{3}  range:  y=((x−4)/(2x−6)) ⇔ x=((6y−4)/(2y−1))  defined for y∈R\{(1/2)} =range of f(x)
$${f}\left({x}\right)=\frac{{x}−\mathrm{4}}{\mathrm{2}{x}−\mathrm{6}} \\ $$$$\mathrm{defined}\:\mathrm{for}\:{x}\in\mathbb{R}\backslash\left\{\mathrm{3}\right\} \\ $$$$\mathrm{range}: \\ $$$${y}=\frac{{x}−\mathrm{4}}{\mathrm{2}{x}−\mathrm{6}}\:\Leftrightarrow\:{x}=\frac{\mathrm{6}{y}−\mathrm{4}}{\mathrm{2}{y}−\mathrm{1}} \\ $$$$\mathrm{defined}\:\mathrm{for}\:{y}\in\mathbb{R}\backslash\left\{\frac{\mathrm{1}}{\mathrm{2}}\right\}\:=\mathrm{range}\:\mathrm{of}\:{f}\left({x}\right) \\ $$

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