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Composition of function: Conditions and Properties - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:34 AM | #JEE Main

Quick Facts

  • Composition of function, Condition for Composite Function, Property of Composite Function is considered one of the most asked concept.

  • 60 Questions around this concept.

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Let $f(x)=2^{10} \cdot x+1 \text { and } g(x)=3^{10} \cdot x-1 \text {. If }(f \circ g)(x)=x$, then x is equal to:

If $\mathrm{f}(\mathrm{x})=\frac{4 \mathrm{x}+3}{6 \mathrm{x}-4}, \mathrm{x} \neq \frac{2}{3}$ and (fof) (x) $\mathrm{g}(\mathrm{x})$, where $\mathrm{g}: \mathbb{R}-\left\{\frac{2}{3}\right\} \rightarrow \mathbb{R}-\left\{\frac{2}{3}\right\}$, then (gogog)(4) is equal to

For $\mathrm{f}(\mathrm{x})$ and $\mathrm{g}(\mathrm{x})$, find the calculation for which $\mathrm{fog}(\mathrm{x})$ can be evaluated.

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Identify the correct statement:

If $(1,2) \in S o R, \mathrm{~S} \& \mathrm{R}$ are 2 relations from B to C and A to B respectively, then there exists $b \in B$, such that:

If $f(x)=\frac{1}{\sqrt{x}}, g(x)=x-2$, then the domain of $f \circ g(x)$ is

If $f=\{(1,2),(3,4),(5,6)\}$ and $g=\{(2,4),(3,5),(4,1)\}$, then the value of $f \circ g(3)+g \circ f(1)$ is

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If P is the number of prime numbers less than or equal to 52, and q is the numbers composite numbers less than or equal to 52, then p + q equals

If f and g are two functions from R to R defined as $f(x)=|x|+x$ and $g(x)=|x|-x$, then fog $(\mathrm{x})$ for $\mathrm{x}<0$ is

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Concepts Covered - 1

Composition of function, Condition for Composite Function, Property of Composite Function

Let $\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B}$ and $\mathrm{g}: \mathrm{B} \rightarrow \mathrm{C}$ be two functions. Then the composition of f and g is denoted by gof and defined as the function gof : $\mathrm{A} \rightarrow \mathrm{C}$ given by $\operatorname{gof}(x)=g(f(x))$

Properties of composition:

In general fog $\neq$ gof (Not commutative)
$\mathrm{fo}(\mathrm{goh})=(\mathrm{fog})$ oh $\quad$ (Associative $)$
If $f$ and $g$ are bijections then fog and gof are also bijections

The composition of any function with the identity function is the function itself. If $f: A \rightarrow B$, then $f o I_A=I_B o f=f$

 

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Composition of function, Condition for Composite Function, Property of Composite Function

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