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3 years ago

What number produces a rational number when added to 1/3

Mathematics

2 answers:

Bingel [31]3 years ago

7 0

Answer:

1/2, 4/3, 1/2, ... any rational number

Step-by-step explanation:

The field of rational numbers is closed under the sum operation. Therefore, if a and b are rational numbers, the number (a + b) is also a rational number.

Consider the rational number a = 1/3, if we add it to any other rational number, the result of that sum will also be a rational number.

Examples:

1/3 + 1/2 = 5/6

1/3 + 4/3 = 5/6

1/3 + 1/6 = 1/2

Verizon [17]3 years ago

6 0

Answer:

Any rational number

Step-by-step explanation:

A <em>rational number</em> is a number obtained by dividing two integers.

Thus, 1/3 is a rational number.

You can add <em>any rational number</em> to 1/3 and the sum will be a rational number.

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What is the inverse of the function below?<br><br> f(x) = 2^x + 6

Helen [10]

The inverse of this function would be f(x) = $\frac{Log(x - 6)}{Log2}$ .

You can find the value of any inverse function by switching the f(x) and the x value. Then you can solve for the new f(x) value. The end result will be your new inverse function. The step-by-step process is below.

f(x) = $2^{x}$ - 6 ----> Switch f(x) and x

x = $2^{f(x)}$ - 6 ----> Add 6 to both sides

x + 6 = $2^{f(x)}$ -----> Take the logarithm of both sides in order to get the f(x) out of the exponent

Log(x + 6) = f(x)Log2 ----> Now divide both sides by Log2

$\frac{Log(x + 6)}{Log2}$ = f(x) ----> And switch the order for formatting purposes.

f(x) = $\frac{Log(x + 6)}{Log2}$

And that would be your new inverse function.

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