Here, the notation
refers to negative infinity, and it indicates that we are including all numbers less than or equal to zero, no matter how small. The set
refers to the set of all real numbers.
Some functions are defined using different equations for different parts of their domain. These types of functions are known as
piecewise-defined functions . For example, suppose we want to define a function
with a domain that is the set of all real numbers such that
for
and
for
We denote this function by writing
When evaluating this function for an input
the equation to use depends on whether
or
For example, since
we use the fact that
for
and see that
On the other hand, for
we use the fact that
for
and see that
Evaluating functions
For the function
evaluate
Substitute the given value for
x in the formula for
For each of the following functions, determine the i. domain and ii. range.
Consider
Since
is a real number for any real number
the domain of
is the interval
Since
we know
Therefore, the range must be a subset of
To show that every element in this set is in the range, we need to show that for a given
in that set, there is a real number
such that
Solving this equation for
we see that we need
such that
This equation is satisfied as long as there exists a real number
such that
Since
the square root is well-defined. We conclude that for
and therefore the range is
Consider
To find the domain of
we need the expression
Solving this inequality, we conclude that the domain is
To find the range of
we note that since
Therefore, the range of
must be a subset of the set
To show that every element in this set is in the range of
we need to show that for all
in this set, there exists a real number
in the domain such that
Let
Then,
if and only if
Solving this equation for
we see that
must solve the equation
Since
such an
could exist. Squaring both sides of this equation, we have
Therefore, we need
which implies
We just need to verify that
is in the domain of
Since the domain of
consists of all real numbers greater than or equal to
and
there does exist an
in the domain of
We conclude that the range of
is
Consider
Since
is defined when the denominator is nonzero, the domain is
To find the range of
we need to find the values of
such that there exists a real number
in the domain with the property that
Solving this equation for
we find that
Therefore, as long as
there exists a real number
in the domain such that
Thus, the range is
Bacteria doesn't produce energy they are dependent upon their substrate in case of lack of nutrients they are able to make spores which helps them to sustain in harsh environments
_Adnan
But not all bacteria make spores, l mean Eukaryotic cells have Mitochondria which acts as powerhouse for them, since bacteria don't have it, what is the substitution for it?
Assimilatory nitrate reduction is a process that occurs in some microorganisms, such as bacteria and archaea, in which nitrate (NO3-) is reduced to nitrite (NO2-), and then further reduced to ammonia (NH3).
Elkana
This process is called assimilatory nitrate reduction because the nitrogen that is produced is incorporated in the cells of microorganisms where it can be used in the synthesis of amino acids and other nitrogen products
There are nothing like emergency disease but there are some common medical emergency which can occur simultaneously like Bleeding,heart attack,Breathing difficulties,severe pain heart stock.Hope you will get my point .Have a nice day ❣️
_Adnan
define infection ,prevention and control
Innocent
I think infection prevention and control is the avoidance of all things we do that gives out break of infections and promotion of health practices that promote life