Question

For what values of the variables are the following expressions defined? 1. 5y+2 2. 18/y 3. 1/x+7 4. 2b/10−b Example: X>7

Answer 1

Answer:

1. All real numbers

2. All real numbers except y = 0

3. All real numbers except x = -7

4. All real numbers except b = 10

Step-by-step explanation:

For any function to be defined at a particular value, it should not be approaching to a value $\infty$ or it should not give us the $\frac{0}{0}$ (zero by zero) form when the input is given to the function.

The value of function will depend on the denominator.

Now, let us consider the given functions one by one:

1. 5y+2

Here denominator is 1. So, it can not attain a value $\infty$ or $\frac{0}{0}$ (zero by zero) form

So, for all real numbers, the function is defined.

$2.\ \dfrac{18}{y}$

At y = 0, the value

$At\ y =0, \dfrac{18}{y} \rightarrow \infty$

So, the given function is defined for all real numbers except y = 0

$3.\ \dfrac{1}{x+7}$

Let us consider denominator:

x + 7 can be zero at a value x = -7

$At\ x =-7, \dfrac{1}{x+7} \rightarrow \infty$

So, the given function is defined for all real numbers except x = -7

$4.\ \dfrac{2b}{10-b}$

Let us consider denominator:

10-b can be zero at a value b = 10

$At\ b =10, \dfrac{2b}{10-b} \rightarrow \infty$

So, the given function is defined for all real numbers except b = 10