Domain of definition

The following functions are defined as follows :

• All polynomial functions are defined over ℝ
• What’s under the square root sign,\(\sqrt{x}\) is defined for x ≥0 ; x  ∈ [0, +∞)
• For y = lnx, x > 0, x ∈ (0 , +∞)
• For  \(\frac{f(a)}{f(b)}\); f(b) ≠ 0

Rationalization

Rationalize \(\frac{1}{\sqrt[3]{5}}\)

\(\frac{1}{\sqrt[3]{5}}\) = \(\frac{1}{\sqrt[3]{5}}\) × \(\frac{\sqrt[3]{5^2}}{\sqrt[3]{5^2}}\) = \(\frac{\sqrt[3]{5}}{5}\)

Gradient and Normal

If the gradient of a tangent is m and the gradient of the normal is m₁ , then

m× m₁= -1

Functions