Answer:
<em>The only value that is in the domains of both functions is 0</em>
<em>The range of g(x) is all values less than or equal to 0</em>
Step-by-step explanation:
As the original function is
Since, domain is the set of all possible input values that define the function, and range is the set of all possible output values for all possible domain values for which the function is defined.
- The domain of
will be [0, ∞)
- The range of
Please check the attached <em>figure a</em> for visualizing the graph of .
<u><em>Impact of double transformation:</em></u>
- When the function
after first transformation
- After the second transformation across y-axis, the function
For
must be equal to or greater than zero for
to be defined i.e. -x ≥ 0.
So,
-x ≥ 0 can be written as x≤ 0
So,
- The domain of
will be (∞, 0]
- The range of
Please check the attached figure a for visualizing the graph of .
So, from the above discussion, we can say that
- 0 is the only that is in the domain of both function.
- The range of g(x) is all values less than or equal to 0
So,
Only two statements are true about the functions f(x) and g(x) are true which are:
<em>The only value that is in the domains of both functions is 0</em>
<em>The range of g(x) is all values less than or equal to 0</em>
<em>Keywords: graph, function</em>
<em>Learn more about graph and function from brainly.com/question/11152594</em>
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