Which one of the following is correct in respect of $f(x) = \frac{1}{\sqrt{|x| - x}}$ and $g(x) = \frac{1}{\sqrt{x - |x|}}$?
Consider the following for the next two (02) items that follow:
Let $f(x)$ and $g(x)$ be two functions such that $g(x) = x - \frac{1}{x}$ and $f \circ g(x) = x^3 - \frac{1}{x^3}$.
What is $g[f(x) - 3x]$ equal to?
Consider the following for the next two (02) items that follow:
Let $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.
Let $h(x) = \frac{f(x)}{g(x)}$.
Consider the following statements:
1. $f(x)$ is differentiable for all $x < 0$
2. $g(x)$ is continuous at $x = 0.0001$
3. The derivative of $g(x)$ at $x = 2.5$ is 1
Which of the statements given above are correct?
Consider the following for the next two (02) items that follow :
Let $3f(x) + f\left(\frac{1}{x}\right) = \frac{1}{x} + 1$
What is $f(x)$ equal to?