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Olegator [25]
3 years ago
9

For f(x)= 3x+1 and g(x)= x^2-6, find (g/f)(x).

Mathematics
2 answers:
o-na [289]3 years ago
4 0
D. The exclusion is important because we cannot divide by zero. Apart from that we are simply looking at a function. 
Anton [14]3 years ago
3 0

Answer:

A. \frac{x^2+6}{3x+1}, x\neq -\frac{1}{3}

Step-by-step explanation:

Given functions,

f(x) = 3x + 1

g(x) = x^2 - 6

∵ (\frac{g}{f})(x) = \frac{g(x)}{f(x)}

By substituting the values,

(\frac{g}{f})(x)=\frac{x^2-6}{3x+1}

Which is a rational function,

We know that,

A rational function is defined for all real numbers except those for which denominator = 0,

If 3x+1 = 0

\implies 3x = -1

\implies x =-\frac{1}{3}

i.e. domain restriction of g/f is x≠ -1/3

Hence, OPTION D is correct.

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3 years ago
Read 2 more answers
Write the equation of the circle with center (5, 1) and radius r = 10
kherson [118]
The standard equation for the circle is:

(x-h)^2+(y-k)^2=r^2, where (h,k) is the center of the circle and r is the radius.

We are given that the center is (5,1) and r=10 so

(x-5)^2+(y-1)^2=100
4 0
3 years ago
If salt (5.99 × 10–6 mol) is dissolved in 1.50 × 10–2 l of water, which expression can be used to find the molarity of the resul
kolezko [41]

The molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

<h3>Molarity of a solution</h3>

From the question, we are to determine the molarity of the resulting solution

From the given information,

Number of moles = 5.99 × 10⁻⁶ mol

Volume = 1.50 × 10⁻² L

Using the formula,

Molarity = Number moles / Volume

∴ Molarity = (5.99 × 10⁻⁶) / (1.50 × 10⁻²)
Molarity = 3.99 × 10⁻⁴ M

Hence, the molarity of the resulting solution is 3.99 × 10⁻⁴ M. The correct option is the third option 3.99 × 10⁻⁴ M

Learn more on Calculating molarity here: brainly.com/question/23051191

#SPJ1

5 0
2 years ago
A triangle has a perimeter of 48 feet. If the three sides of the triangle are n, 4n−2, and 4n−4, what is the length of each side
alexdok [17]

Answer:

6; 22; 20 (ft.)

Step-by-step explanation:

1) if the length of the each side are: n; 4n-2 and 4n-4, then the expression of the perimeter can be written: P=n+4n-2+4n-4 or P=9n-6.

2) if according to the condition perimeter is 48 (ft.), then

9n-6=P; ⇔ 9n-6=48; n=6.

3) if n=6, then the required lengths of the sides are:

n=6 (ft.);

4n-2=22 (ft.);

4n-4=20 (ft.)

3 0
3 years ago
On any day, the probability of rain is 0.3. The occurrence of rain on any day is independent of the occurrence of rain on any ot
poizon [28]
<h3>Answer: 0.47178  Step-by-step explanation: Find the probability for each p(X=x) up to 5 using the equation: (x-1)C(r-1)*p^r * q^x-r, where x is number of days, p = .3 (prob of rain). q=.7 (prob of not rain), and r=2 (second day of rain). also C means choose. So p(X=1) = 0 p(X=2) = 1C1 * .3^2 * .7^0 = .09 P(X=3) = 2C1 * .3^2 * .7^1 = .126 P(X=4) = 3C1 * .3^2 * .7^2 = .1323 P(X=5) = 4C1 * .3^2 * .7^3 = .12348 Then add all of them up 0+.09+.126+.1323+.12348 = .47178</h3>
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3 years ago
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