Are the functions f(x) and g(x) inverse of one another?
1 answer:
<h2>Answer:</h2><h2></h2><h3>No!</h3><h2></h2><h2>Explanation:</h2><h2></h2>
The function doesn't have inverse because it doesn't pass the horizontal line test. This test tells us that a function
has an inverse function<em> if and only if</em> there is no any horizontal line that intersects the graph of
at more than one point. As you can see, from the graph of f (the red one), if you draw an horizontal line that passes through
then this line will touch the graph of f at three points, so the horizontal line test is not satisfied here. If you see the graph of g, this doesn't represent a function because there is at least one vertical line that touches the graph at more than one point, so this relation is not a function.
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Answer:
--- Objective function
Interval =
Step-by-step explanation:
Given
Represent the number with x
The required sum can be represented as:
Hence, the objective function is:
To get the the interval, we start by differentiating w.r.t x
<em>Using first principle, this gives:</em>
Equate S'(x) to 0 in order to solve for x
Subtract 1 from both sides
Multiply both sides by -1
Cross Multiply
Take positive square root of both sides because x is positive
Representing x using interval notation, we have
Interval =
To get the smallest sum, we substitute 1 for x in
<em>Hence, the smallest sum is 2</em>