For what values of the variables are the following expressions defined? A) 5y+2 B)8/y C)1/x+7 D)2b/10-b

A) All real numbers

B) All real numbers except y = 0

C) All real numbers except x = -7

D) All real numbers except b = 10

Step-by-step explanation:

An expression is defined at all those points at which it does not give the value equal to or does not give the zero by zero form.

i.e. Numerator and Denominator both having zeroes.

Now, let us have a look at the given expressions:

A) 5y+2

Here, Denominator is 1. So, there is no constraint on the value of y.

Hence, at all Real Numbers, the expression is defined.

Here, denominator is y,

At , the value of expression will approach towards

Hence, this expression is defined at All Real numbers except y = 0

Here, zero by zero form is not possible.

Let us check the value of x where the denominator can be 0 and as a result the expression tends to reach value .

x+7=0

At x = -7, the denominator will be 0 and as a result the expression tends to reach value .

Hence, the expression is defined at All real number except x = -7

Here zero by zero form is not possible.

Let us check the value of b where the denominator can be 0 and as a result the expression tends to reach value .

10-b=0

At b = 10, the denominator will be 0 and as a result the expression tends to reach value .

Hence, the expression is defined at All real number except b = 10