Let f(x)=3x2−5x+13 and g(x)=2x−7 . What is g(f(x)) ?
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Answer:
is an even function.
Step-by-step explanation:
Recall when it means when a function is even or odd. An even function has the following property:
And an odd function has the following property:
So, let's test some values for cos(x).
Let's use π/3:
From the unit circle, was can see that this is 1/2 (refer to the x-coordinate).
Now, let's find -π/3. This is the same as 5π/3. Thus:
And again from the unit circle, we can see that this is 1/2.
Therefore, despite the negative, the function outputs the same value.
Cosine is an even function.
Notes:
Cosine is an even function and sine is an odd function. It's helpful to remember these as they can help you solve some trig problems!