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There are several ways to prove a mathematical statement. These ways include: by contradiction, by induction, contraposition, etc
<h3>How to prove the statement by contradiction</h3>To prove the statement, we make use of proof by contradiction
From the question:
x is a composite number such that: x > 1
This means that 1 < a < x is a factor of x
This can be represented as:
Where:
- a and b are positive integers
- 1 < a, b < x
Assume that b is less than or equal to a.
Also, let
This means that:
The above becomes
Rewrite as:
So, we have:
The above means that:
The above inequality is a contradiction because, a number x cannot be greater than itself
This means that, the supposition is wrong.
Hence, the given statement has been proved by contradiction
Read more about proof by contradiction at:
Answer:
A) f(x) has y-intercept at and g(x) has y-intercept at (0,0)
B) f(x) has asymptote as x= 0 and g(x) has asymptote as x= 4.
Step-by-step explanation:
The functions given are and the graph of g(x).
A): Since, <em>'y-intercepts are the points where the graph of the function cuts y-axis' </em>
<em>So, 'at x=0, we obtain y-intercepts'.</em>
Thus,
implies
Hence, is the y-intercept of f(x).
Now, we see that,
The graph of the function g(x) crosses y-axis at the point (0,0).
Hence, the (0,0) is the y-intercept of the function g(x).
B): As we know, <em>'asymptotes are the lines that approaches the curves but does not meet them'. </em>
As, the numerator of f(x) is of lower degree than the denominator.
We have, the function f(x) has x= 0 as the horizontal asymptote.
Further, graph of g(x) gives us, 'the line x= 4 is the asymptote'.
Hence, the function g(x) has vertical line x= 4 as the asymptote.