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Mathematics

1 answer:

LuckyWell [14K]2 years ago

4 0

Answer:

(x,y)--> (x+4,y-4)

Step-by-step explanation:

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Find (f/g) (x) and state the domain restriction. f (x) = 6x - 3 and g(x) = 12x^2 - 6x

Rufina [12.5K]

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Answer:

(f/g)(x) = 1/(2x)

x ≠ 1/2

Step-by-step explanation:

$(f/g)(x)=\dfrac{f(x)}{g(x)}=\dfrac{6x-3}{12x^2-6x}=\dfrac{6x-3}{2x(6x-3)}\\\\\boxed{(f/g)(x)=\dfrac{1}{2x}}\quad x\ne\dfrac{1}{2}$

The domain restriction x ≠ 1/2 comes from the requirement to prevent the denominator factor 6x-3 from being zero.

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Factor this equation<br> 4x^2+12x-7

Levart [38]

$4x^2+12x-7=0\\\\a=4;\ b=12;\ c=-7\\\Delta=b^2-4ac\\\\\Delta=12^2-4\cdot4\cdot(-7)=144+112=256 \ \textgreater \ 0\\\\therefore\\x_1=\dfrac{-b-\sqrt\Delta}{2a}\ and\ x_2=\dfrac{-b+\sqrt\Delta}{2a}\\\\\sqrt\Delta=\sqrt{256}=16\\\\x_1=\dfrac{-12-16}{2\cdot4}=\dfrac{-28}{8}=\boxed{-\dfrac{7}{2}}\\\\x_2=\dfrac{-12+16}{2\cdot4}=\dfrac{4}{8}=\boxed{\dfrac{1}{2}}$