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Nady [450]
3 years ago
11

Identify The domain of the rational function, g(x)= 1/x+3

Mathematics
1 answer:
8_murik_8 [283]3 years ago
4 0

Answer:

The domain is (-∞ , -3) ∪ (-3, ∞) ⇒ D

Step-by-step explanation:

<em>The domain of the rational fraction is t</em><em>he values of x which make the fraction defined</em><em>. That means </em><em>the domain does not contain the values of x which make the denominator equal to 0</em><em>.</em>

∵ g(x) = \frac{1}{x+3}

∴ The denominator = x + 3

→ Equate the denominator by 0

∵ x + 3 = 0

→ Subtract 3 from both sides

∴ x + 3 - 3 = 0 - 3

∴ x = -3

→ That means the domain can not have -3 because it makes the denominator

   equal to 0

∴ The domain is all values of real numbers except x = -3

∴ The domain = {x : x ∈ R, x ≠ -3}

∴ The domain = (-∞ , -3) ∪ (-3, ∞)

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Find the x-and y-intercepts of the graph of the function f(x) = x^4 − 1

Answer: The given equation is

f(x) = x^{4} - 1

x- and y-intercept of the graph of the function f(x) = x^4 - 1 is

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

A graph of the above point is attached

Step-by-step explanation:

Given equation, f(x) = x^{4} - 1

let's assume the above equation with respect to y to find intercept i.e

y = x^{4} - 1 .........................(i)

Now, for the x-intercept put y = 0 in eq.(i)

So, we get,

0 = x^4 - 1

x^4 = 1

x = -1, +1

from above we get the x-intercept (1,0), (−1,0)

Now, for the y-intercept put x = 0 in eq.(i)

So, we get

y = 0^4 - 1

y = -1

from above we get the y-intercept (0, -1)

Therefore, from all above

  1. x- and y-intercept of the given equation f(x) = x^4 - 1 is

x-intercept(s): (1,0), (−1,0)

y-intercept(s): (0, −1)

Graph of the given equation f(x) = x^4 - 1 with intercept is

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What are the solution to the system of equations graphed below?
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Step-by-step explanation:

u need to look where the lines intercept and im doing this in my math class now so my teacher said wherever the lines intercept u need to take the points where they intercept at so for this one it would be (4,8) and the other is (0,-8)

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