Question

Compare the two functions n2 and 2n /4 for various values of n. Determine when the second becomes larger than the first.

Answer 1

hey mate
here's the solution

Answer 2

Answer:

Let,

$f(n) = n^2$ and $g(n) = \frac{2n}{4}$

Since, f(n) is a quadratic function,

So, its domain = set of all real numbers,

Also, the vertex of f(n) = (0,0) where f(n) is an upward parabola,

Thus, range of f(n) = All real numbers greater than 0,

While, g(n) is a line,

Domain = Set of all real numbers,

Range of g(n) = Set of all real numbers,  ( the range of a linear function is always R )

If g(n) > f(n)

$\frac{2n}{4} > n^2$

$\frac{1}{2} > n$

That is, for all real values less than 1/2, g(n) is greater than f(n).

If g(n) < f(n),

$\frac{2n}{4} < n^2$

$\frac{1}{2} < n$

That is, for all real values greater than 1/2, f(n) is greater than g(n).