What is the domain of the step function f(x) = ⌈2x⌉ – 1?
2 answers:
<h2>Answer:</h2>
The domain of the given step function is:
The set of all the real numbers.
<h2>Step-by-step explanation:</h2><u>Ceiling function--</u>
The ceiling function also known as the least integer function is the function which takes the largest value of the integer for a non-integer number which lie between the two integers , and gives the integer itself if the number is integer.
and it is given by:
(
For example--
if x= 0.5
then f(x)=1 since x lie between 0 and 1
if x= -2.5
Then f(x)= -2
since x lie between -3 and -2.
if x=3
then f(x)=3 )
Also, the function is defined for all real values of x.
i.e. The domain of such a function is: All real numbers.
The function f(x) is given by:
Hence, the domain is all the real numbers.
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Answer:
As you can see, the difference between the reciprocal of and the inverse of
is that
and
.
Step-by-step explanation:
First lets find both the reciprocal of and the inverse of
Recall that the reciprocal of a value is where you take a fraction and swap the places of the terms. In the case of , 1 is the denominator, so
To find the inverse of a function, you first need swap the locations of x and y in the equation
Now, you need to solve for y
Now, lets rewrite each of these to better compare them
As you can see, the difference between the reciprocal of and the inverse of