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10 months ago

Given 3x^2+x-4/x-1 what are the domain and range

Mathematics

1 answer:

Katarina [22]10 months ago

6 0

Answer:

doman: x ≠ 1
range: y ≠ 7

Step-by-step explanation:

The domain is the horizontal extent of the graph, the set of x-values for which the function is defined. The range is the vertical extent of the graph, the set of y-values defined by the function.

<h3>Simplified</h3>

The given function is undefined where its denominator is zero, at x=1. Everywhere else, it can be simplified to ...

$\dfrac{3x^2+x-4}{x-1}=\dfrac{(x-1)(3x+4)}{(x-1)}=3x+4\quad x\ne 1$

<h3>Domain</h3>

The simplified function (3x+4) is defined for all values of x except x=1. The simplest description is ...

x ≠ 1

In interval notation, this is ...

(-∞, 1) ∪ (1, ∞)

<h3>Range</h3>

The simplified function is capable of producing all values of y except the one corresponding to x=1: 3(1)+4 = 7. The simplest description is ...

y ≠ 7

In interval notation, this is ...

(-∞, 7) ∪ (7, ∞)

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Solve the system of linear equations below. <br><br> X+y=4<br> 2x+3y=0

deff fn [24]

X + y = 4...x = 4 - y

2x + 3y = 0
2(4-y) + 3y = 0
8 - 2y + 3y = 0
-2y + 3y = 0 - 8
y = -8

x + y = 4
x - 8 = 4
x = 4 + 8
x = 12

solution is : (12,-8)

7 0

2 years ago

Read 2 more answers

How do I solve this?

bogdanovich [222]

Answer:

Step-by-step explanation:

$5(x+7)^4=\boxed5\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\cdot(x+7)\cdot(x+7)\\\\35(x+7)^2=\boxed5\cdot7\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\\\\15(x+7)^3=\boxed5\cdot3\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\cdot(x+7)\\\\GCF\bigg(5(x+7)^4,\ 35(x+t)^2,\ 15(x+7)^3\bigg)=\boxed5\cdot\boxed{(x+7)}\cdot\boxed{(x+7)}\\\\=5(x+7)^2$

5 0

2 years ago

What is the LCM of x^2+5 and x^2+10x+25?

avanturin [10]

Answer:

(x+5)²(x²+5)

Step-by-step explanation:

Given two functions x²+5 and x²+10x+25, to get their Lowest common factor, we need to to first factorize x²+10x+25

On factorising we have:

x²+5x+5x+25

= x(x+5) +5(x+5

= (x+5)(x+5)

= (x+5)²

The LCM can be calculated as thus

| x²+5, (x+5)²

x+5| x²+5, (x+5)

x+5| x²+5, 1

x²+5| 1, 1

The factors of both equation are x+5 × x+5 × x²+5

The LCM will be the product of the three functions i.e

(x+5)²(x²+5)

This hives the required expression.

5 0

2 years ago

I need help with this.

alekssr [168]

Answer:

x=7

Step-by-step explanation:

8 0

1 year ago

Find the center and radius of the circle with the given equation. Then select the correct graph of the equation.

likoan [24]

Answer:

Step-by-step explanation:

In order to find the center and the radius of this circle, you have to complete the square on it. And only for the x-terms, because the y term is squared and there is no other y term. We'll get to that in a second.

Take half the linear x-term, square it and add it to both sides. Our linear term is 10. Half of 10 is 5, and 5 squared is 25. We add 25 to both sides:

The reason we do this is to create a perfect square binomial inside that set of parenthesis. Simplifying the right side as well gives us:

This tells us that the center is (-5, 0). Remember when I said we would get back to the y terms? Because there was only a y-squared and no other y terms, that is the same as writing the equation as

The radius is the square root of the constant. So the radius is 6.

D is the graph you want.

3 0

2 years ago