https://r2.erweima.ai/mathbot/image/1726534731563p2d59pkz.pdf

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1. Determine the domain of functions such as:
   - \( f(x) = 1 + 55x - 2 \)
   - \( g(x) = x - 10 \)
   
2. Operations with functions:
   - Given \( f(x) = x^2 - 3x \) and \( g(x) = 2x + 1 \), perform operations like \( (f + g)(x) \), \( (fg)(x) \).

3. Prove injectivity and surjectivity for functions like:
   - \( f(x) = x^3 \) (prove it is bijective).

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Explore detailed step-by-step solutions to problems related to determining the domain of functions, performing operations with functions, and proving injectivity and surjectivity. This guide covers concepts such as function domains, injective and surjective proofs, and operations like addition and multiplication of functions. Ideal for students in Grades 10-12.

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