Explanation:
Refer to the table below. I've added a third row where I multiplied each x value with its corresponding frequency value f. We can refer to this row as the xf row.
Once we know the xf values, we add them up to get 245.
We'll then divide that result over the sum of the frequency values (add everything in the second row). The sum of the frequency values is 39.
So the mean is approximately: 245/39 = 6.282051 which rounds to 6.282
Notice that this mean value is fairly close to the x value which has the highest frequency.
Answer:
Step-by-step explanation:
Given that:
f(x) approaches 150, and
g(x) approaches 0, with g(x) < 0,
as x approaches 3.
This means:
We need to evaluate:
Distributing the limit to numerator and denominator, we get:
The expression will result in infinity as the answer, but since, g(x) < 0, this means g(x) is approaching 0 from the negative side. As a result, the expression 150/0 will approach negative infinity as x will approach 3.
Therefore, we can conclude:
Answer: The correct option is
(a) f(n) = n - 1.
Step-by-step explanation: We are given to determine whether the given functions are one-to-one or not.
We know that a function y = f(x) is one-to-one if and only if
f(x) = f(y) ⇔ x = y.
That is, any two distinct elements cannot have the same image.
(a) The given function is
Let us consider that
Similarly,
So, this function is one-to-one.
(b) The given function is
Let us consider that
That is, there may be two unequal elements having same image.
For example, f(-1)=(-1)²+1=1+1=2, f(1)=(1)²+1=1+1=2.
It implies that f(-1)=f(1) but 1 ≠ -1.
So, the given function is not one-to-one.
(c) The given function is
Here, the image of all the elements is 1.
For example,
f(2)=f(3) but 2≠3.
So, more than one element is having the same image and so the function cannot be one-to-one.
(d) The given function is
Here, we see that
So, f(2)=f(3) but 2≠3.
So, the given function is not one-to-one.
Thus, the correct option is (a).