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Korolek [52]
4 years ago
10

Solve the simultaneous equations y=x-2 and y=3x+5

Mathematics
1 answer:
IgorLugansk [536]4 years ago
3 0

Answer:

(- 3.5, - 5.5 )

Step-by-step explanation:

Given the 2 equations

y = x - 2 → (1)

y = 3x + 5 → (2)

Substitute y = 3x + 5 into (1)

3x + 5 = x - 2 ( subtract x from both sides )

2x + 5 = - 2 ( subtract 5 from both sides )

2x = - 7 ( divide both sides by 2 )

x = - 3.5

Substitute x = - 3.5 into either of the 2 equations and evaluate for y

Substituting into (1)

y = - 3.5 - 2 = - 5.5

Solution is (- 3.5, - 5.5 )

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Given functions f ( x ) = 1 √ x and m ( x ) = x 2 − 4 , state the domains of the following functions using interval notation.
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The domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

<h3>What is a function?</h3>

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have:

f(x) =  1/√x

m(x) = x² - 4

Domain of f(x)/m(x):

f(x)/m(x) = (1/√x)/(x² - 4)

f(x)/m(x) = 1/√x(x² - 4)

The denominator cannot be zero:

√x(x² - 4) ≠ 0

x(x - 2)(x+2) ≠ 0

x ≠ 0, 2, -2

and x > 0

Domain of f(x)/m(x) is:   (0, ∞) - {0, 2, -2} or \:\left(0,\:2\right)\cup \left(2,\:\infty \:\right)

Domain of f(m(x)):

f(m(x)) = 1/√(x² - 4)

x² - 4 > 0

Domain: \rm \left(-\infty \:,\:-2\right)\cup \left(2,\:\infty \:\right)

Domain of m(f(x)):

= ((1/√x)² - 4)

Domain: \:\left(0,\:\infty \:\right)

Thus, the domain of a function f(x)/m(x) = 1/√x(x² - 4) is (0, ∞) - {0, 2, -2} for other function is shown in the solution.

Learn more about the function here:

brainly.com/question/5245372

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Step-by-step explanation:

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