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nlexa [21]
3 years ago
6

Can someone help me please? Thanks! Please show your work and explain.

Mathematics
1 answer:
Liono4ka [1.6K]3 years ago
6 0
1 Simplify 1/2x^2 to x^2/2
X^2/2 - x+5=0
2 Use the Quadratic Formula
x=1+3ı,1−3ı
So the answer is the first one a
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What is the range of the following function:<br> y = 2(5^x) - 1
Orlov [11]
<h2>Hello!</h2>

The answer is:

The range of the function is:

Range: y>2

or

Range: (2,∞+)

<h2>Why?</h2>

To calculate the range of the following function (exponential function) we need to perform the following steps:

First: Find the value of "x"

So, finding "x" we have:

y=2(5^{x}-1)\\\frac{y}{2}=5^{x}-1\\\\\frac{y}{2}-1=5^{x}\\\\Log_{5}(\frac{y}{2}-1)=Log_5(5^{x})\\\\x=Log_{5}(\frac{y}{2}-1)

Second: Interpret the restriction of the function:

Since we are working with logarithms, we know that the only restriction that we found is that the logarithmic functions exist only from 0 to the possitive infinite without considering the number 1.

So, we can see that if the variable "x" is a real number, "y" must be greater than 2 because if it's equal to 2 the expression inside the logarithm will tend to 0, and since the logarithm of 0 does not exist in the real numbers, the variable "x" would not be equal to a real number.

Hence, the range of the function is:

Range: y>2

or

Range: (2,∞+)

Note: I have attached a picture (the graph of the function) for better understanding.

Have a nice day!

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Step-by-step explanation:

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exis [7]

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1) Multiply that number by 100.

2) Add the percent sign % to it.

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Step-by-step explanation:

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