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

An expression is defined at all those points at which it does not give the value equal to [tex]\infty[/tex] or does not give the zero by zero form.

i.e. [tex]\frac{0}{0}[/tex] 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.

[tex]B)\ \dfrac{8}{y}[/tex]

Here, denominator is y,

At [tex]y = 0[/tex], the value of expression will approach towards [tex]\infty[/tex]

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

[tex]C)\ \dfrac{1}{x+7}[/tex]

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 [tex]\infty[/tex].

x+7=0

At x = -7, the denominator will be 0 and as a result the expression tends to reach value [tex]\infty[/tex].

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

[tex]D) \dfrac{2b}{10-b}[/tex]

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 [tex]\infty[/tex].

10-b=0

At b = 10, the denominator will be 0 and as a result the expression tends to reach value [tex]\infty[/tex].

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