If f f f maps the set of natural numbers to whole numbers such that f ( x y ) = f ( x ) f ( y ) + f ( x ) + f ( y ) f(xy) = f(x)f(y) + f(x) + f(y) f (...

Determine the range of values for which the function $$ y = \sqrt{x - 2} + \sqrt{8 - x} $$ is defin...

Find the minimum value of the function $$ f(x) = \log_2(x^2 - 2x + 5) $$. ...

If $$ f(x) $$ is an odd function, the graph $$ y = f(x) $$ will be symmetric about which point or a...

If $$ u(t) = 4t - 5 $$, $$ v(t) = t^2 $$, and $$ f(t) = \frac{1}{t} $$, find the formula for $$ u(f(...

Determine the domain of the function: $$ y = \sqrt{\frac{x - 3}{x + 3}} + \sqrt{\frac{1 - x}{1 + ...

For any non-zero real number $$ x $$, let $$ f(x) + 2f\left(\frac{1}{x}\right) = 3x. $$ Then, ...