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VladimirAG [237]
3 years ago
15

What are the domain and range of the logarithmic function f(x) = log7x? Use the inverse function to justify your answers.

Mathematics
2 answers:
kolezko [41]3 years ago
5 0
The domain  is  x > 0  or (0,∞)

the range is  f(x) >= 0

the inverse of the function is  f-1(x)= (10^x ) / 7 

here we see that domain is >= 0  which is the range of f(x) and the range is > 0 whch equals the domain of f(x)

    
snow_tiger [21]3 years ago
3 0

We have been given the function

f(x)=\log 7x

Domain is the set of x values for which the function is defined. We know that a logarithm function is defined for all values greater than zero.

Thus, for the domain , we have

7x>0\\x>0

The domain is given by \left \{ x \in R, x>0 \right \}

The range is the set of y values for which the function is defined. For this logarithm function, we can take any values. Hence, the range of the function is all real number.

Now let us find the inverse of the function.

y=\log (7x)\\ \text{Swap x and y, we get}\\ x=log(7y)\\ \text{Now, we find the value of y}\\  7y=10^x\\ y=\frac{1}{7}10^x\\ f^{-1}(x)=\frac{1}{7}10^x

The domain of the inverse function is all real number and range is all values greater than zero.

We know that the domain of the function is range of the inverse function and the range of the function is domain of the inverse function.

Therefore, it justifies our solution.

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Step-by-step explanation:

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y = 4.3

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Hey Siri Council consist of eight Democrats and five Republicans if a committee of five people are selected find the probability
Flura [38]

Answer:

55/2574 ≈ 2.18%

Step-by-step explanation:

There are a total of 13 people on the council.

The probability that the first person is a Democrat is 8/13.

The probability that the second person is a Democrat is 7/12.

The probability that the third person is a Republican is 5/11.

The probability that the fourth person is a Republican is 4/10.

The probability that the fifth person is a Republican is 3/9.

The total probability is:

P = (8/13) (7/12) (5/11) (4/10) (3/9)

P = 56/2574

P ≈ 0.0218

There is a 2.18% probability of selecting two Democrats and three Republicans.

6 0
3 years ago
Point B is on line segment AC. Given AB=4x-6, AC=2x+10, and BC=4, determine the numerical length of AC
kvv77 [185]

Answer:

AC = 22

Step-by-step explanation:

AB + BC = AC , substitute values

4x - 6 + 4 = 2x + 10 , that is

4x - 2 = 2x + 10 ( subtract 2x from both sides )

2x - 2 = 10 ( add 2 to both sides )

2x = 12 ( divide both sides by 2 )

x = 6

Then

AC = 2x + 10 = 2(6) + 10 = 12 + 10 = 22

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finlep [7]

Answer:

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