Express the function G in the form f∘g. (Enter your answers as a comma-separated list. Use non-identity functions for
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Given:
The given function is:
To find:
The range of the given function.
Solution:
We have,
It is a quadratic function because the highest power of the variable x is 2.
Here, the leading coefficient is -32 which is negative. So, the graph of the given function is a downward parabola.
If a quadratic function is , then the vertex of the quadratic function is:
In the given function, .
The value of the given function at is:
The vertex of the given downward parabola is . It means the maximum value of the function is
. So,
Therefore, the range of the given function is .