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Composition of function: Conditions and Properties - Practice Questions & MCQ
Edited By admin | Updated on Sep 18, 2023 18:34 AM | #Sastra University B.Tech Admission
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Composition of function, Condition for Composite Function, Property of Composite Function is considered one of the most asked concept.
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41 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
Concepts Covered - 1
Composition of function, Condition for Composite Function, Property of Composite Function
Let f: A B and g : B
C be two functions. Then the composition of f and g is denoted by gof and defined as the function gof : A
C given by gof (x) = g(f (x))
Properties of composition:
- In general fog ≠ gof (Not commutative)
- fo(goh) = (fog)oh (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
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