Dear learner, I hope the lesson provides you a clear and intersting contents with simple demonstration style. here you will get the main contents of the lesson with buletins. have a nice reading!

• Let $f \colon \mathbb{A} \to \mathbb{B}$    and $g \colon \mathbb{B} \to \mathbb{C}$ be functions , then the function h(x) defined by $h(x)$ = $g(f(x))$ = $(gof)(x)$ for all $x \in \mathbb{A}$ and f(x) is in the domain of g is the composition of g by f denoted by $(gof)(x)$ = $g(f(x))$
• Let $f$ be a function, if its inverse is also a function, then we say $f$ is inversible and its inverse is denoted by $f^{-1}$.
• steps to find $f^{-1}$:
• let $f$ be an invertible function in the set of real numbers and $f^{-1}$ be a fumnction, then graph of $f$ and $f^{-1}$ are mirror images of each other with respect to the line $y = x$.
• the production cost and amount of production are proportional
• the distance covered by the moving body and time it takes to complete that distance are proportional