Unit-I: Sets and Functions
Unit-II: Algebra
Unit-III: Coordinate Geometry
Unit-IV: Calculus
Unit-V: Mathematical Reasoning
Unit-VI: Statistics and Probability

Composition of functions

If f: X \rightarrow Y and  g: Y\rightarrow Z, then the composition of  f and  g denoted by \text {gof } (‘  g composite  f ‘) is defined by 

 (\text {gof })(x)=g (f(x)), x \in X

\text { dom }(\text {gof})=x and \text {rng} (\text {gof})=g (\text {rng f})\subseteq Z

Example:

 f_1(x)=\sin x^2

g(x)= \sin x, f(x)=x^2 then (\text {gof})(x)=g(f(x))

 \begin{aligned} g(f(x))&=g(y)\\&=\sin y\\&=\sin x^2\\&=f_1(x)\end{aligned}

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