The domain of the given function is the set of all the real numbers.
Explanation of Solution
Given information:
Given function
f(x)=2int(x)
Calculation:
The domain of the function f(x) , is the set of all the possible values of x .
The value of the function f(x) is given by 2int(x) . The greatest integer less than or equal to x is multiplied by 2. This operation can be performed on any real number.
So, the domain of x is the set of all the real numbers.
Therefore, the domain of the given function is the set of all the real numbers.
(b)
To determine
To locate: any intercepts of the given function.
(b)
Expert Solution
Answer to Problem 39AYU
The x intercept is (x,0) for, 0≤x<1 .
Explanation of Solution
Given information:
Given function
f(x)=2int(x)
Calculation:
The x intercepts are those points for which y coordinate is zero and the y intercepts are those points for which the x coordinate is zero.
The value of the function f(x) of the coordinate, when 0≤x<1 is 0.
Therefore, the x intercept is (x,0) for, 0≤x<1 .
(c)
To determine
To sketch: the graph of the given function.
(c)
Expert Solution
Explanation of Solution
Given information:
Given function
f(x)=2int(x)
Calculation:
Graph the greatest integer function, f(x)=2int(x) . Substitute some values for x in the equation to obtain few points on the graph.
xy=2int(x)(x,y)
1 2
(1,2)−2 4
(−2,4) -1 −2(−1,−2)
Plot the points and draw the lines to get the graph of the function.
(d)
To determine
To find: the range based on the graph.
(d)
Expert Solution
Answer to Problem 39AYU
The range of f is the set of even integers.
Explanation of Solution
Given information:
Given function
f(x)=2int(x)
Calculation:
The points on the graph of f have all the y coordinates as even integers. For each number y , there is at least one number x in the domain.
So, the range of f is the set of even integers.
(e)
To determine
To find: whether f continuous on its domain or not.
(e)
Expert Solution
Answer to Problem 39AYU
The function f is discontinuous on its domain.
Explanation of Solution
Given information:
Given function
f(x)=2int(x)
Calculation:
From the graph, it can be observed that there is a discontinuity at x=0,1,2,... . So, the function f is discontinuous on its domain.
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