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3 years ago

Find the domain for the rational function f(x)=x-1/x+3

Mathematics

1 answer:

Savatey [412]3 years ago

4 0

Answer:

x≠-3 or x<-3 and -3<x or (∞,-3) and (-3,∞)

Step-by-step explanation:

If the expression you have given is $\frac{x-1}{x+3}$ then the domain is x≠-3

This is because in a function that is a fraction the denominator can never equal 0, otherwise you are dividing by 0 which is undefined.

Here the denominator is x+3 and so to find the undefined value of x:

Set x+3 equal to 0:

x+3=0

Subtract 3:

⇒ x=-3

That value is undefined since it results in the division of 0 which also means that it is not in the domain.

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Which two values of x are roots of the polynomial below? x^2-3x+5

Gemiola [76]

Given:

Polynomial $x^2-3x+5$

To find:

The values of x.

Solution:

$x^2-3x+5=0$

Quadratic equation formula:

$$x=\frac{-b \pm \sqrt{b^{2}-4 a c}}{2 a}$

Here $a=1, b=-3, c=5$ .

Substitute the values in the formula, we get

$$x=\frac{-(-3) \pm \sqrt{(-3)^{2}-4 \cdot 1 \cdot 5}}{2 \cdot 1}$

$$x=\frac{3 \pm \sqrt{9-20}}{2}$

$$x=\frac{3 \pm \sqrt{-11}}{2}$

$$x=\frac{3 - \sqrt{-11}}{2} \ \text{and} \ x=\frac{3 + \sqrt{-11}}{2}$

Option E and option F are the roots of the polynomial.

The values of x are $x=\frac{3 - \sqrt{-11}}{2} \ \text{and} \ x=\frac{3 + \sqrt{-11}}{2}$ .

7 0

3 years ago

Find which term in the geometric sequence 1,3,9,27,... is the first to exceed 7,000.

Zielflug [23.3K]

The common ratio between terms is 3, so the sequence has general $n$ -th term

$a_n=3^{n-1}$

for $n\ge1$ . The term exceeds 7000 when

$3^{n-1}>7000\implies n-1>\log_37000\implies n>1+\log_37000\approx9.06$

which means the first time $a_n$ exceeds 7000 occurs when $n=10$ . Indeed,

$a_{10}=3^{10-1}=19,683$

while the previous term would have been

$a_9=3^{9-1}=6561$

8 0

3 years ago

Solve for x. Assume that lines which appear tangent are tangent.

Orlov [11]

Answer:

Period. Segment Lengths in Circles. Solve for x . Assume that lines which appear tangent are tangent. 1). 154 2 9 (249). 425 = 9481. 90-144.

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3 years ago

Given the following linear function sketch the graph of the function and find the domain and range f(x)=-3x+7

natka813 [3]

<h3>Answer:</h3>

see attached for a graph

domain and range: all real numbers

<h3>Step-by-step explanation:</h3>

The function is written in slope-intercept form, showing that it has a slope of -3 and a y-intercept of +7. The y-intercept (0, 7) is a point on the line, as is a point 1 unit to the right and down 3 units, (1, 4).

The graph will be the line through these two points.

_____

As with any odd-degree polynomial function, both domain and range are all real numbers: (-∞, ∞).

6 0

3 years ago

Una recta que pasa por los puntos A (2,1) y B (6,3) y otra recta pasa por A y por el punto (0,y) ¿Cuánto vale y, si ambas rectas

ASHA 777 [7]

The translation of the question given is

A line that passes through the points A (2,1) and B (6,3) and another line passes through A and through the point (0, y). What is y worth, if both lines are perpendicular?

Answer:

y = 5

Step-by-step explanation:

Line 1 that passes through A (2,1) and B (6,3)

Slope (m1) = 3-1/6-2 = 2/4 = 1/2

y - 1 = $\frac{1}{2}$ ( x -2)

2y - 2 = x- 2

y = $\frac{x}{2}$

Line 2 passes through A (2,1) and (0,y)

slope (m2) = $\frac{y-1}{-2}$

Line 1 and Line 2 are perpendicular

m1*m2 = -1

$\frac{1}{2}$ * $\frac{y-1}{-2}$ = -1

y-1 = 4

y = 5

slope = -2

Equation of Line 2

Y-1 = -2(x-2)

y -1 = -2x +4

2x +y = 5

7 0

2 years ago