Asked by Winston

Decide if the following pair of functions are of the same order.

(a) f(x) = x^2 - 7 and g(x) = x^2 + 7

I found this example solution online:
a). f(x) = 3x + 7 and g(x) = x
x <= 3x + 7 <= 4x for all x > 7

I need help making sense of this so I can apply it to my work. Thanks.
Answered by Reiny
The highest power term determines the rank of the function
Since both f(x) and g(x) have x^2 as their highest power, that is, they both have 2 as the highest exponent,
they are of the same order.
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