Topic Details (Notes format)

How to Perform Function Composition (f ∘ g)

Subject: Mathematics

Book: Maths Mastery

Function composition f(g(x)) means applying g first, then feeding that result into f. For instance, if f(x)=x²+1 and g(x)=2x–3, then f(g(x))= (2x–3)²+1=4x²–12x+9+1=4x²–12x+10. Composition frequently appears in advanced algebra, transformations, and chain-rule usage in calculus. In real-world models, you might first calculate a cost function g(x), then apply a tax function f to g(x). Mastery of composition fosters advanced manipulations of nested processes and underpins functional decomposition strategies in computing, engineering, or multi-stage transformations.

Practice Questions

What is the square root of 121?

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What is the sum of the first 50 positive integers?

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If 2x - 3 = 7, what is the value of x?

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If x² - 9x + 18 = 0, what are the roots of the equation?

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If the product of two numbers is 120 and their sum is 26, what are the numbers?

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A cone has a base radius of 7 cm and height of 24 cm. What is its volume?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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The sum of the squares of two consecutive integers is 145. What are the integers?

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If sin(x) = 3/5 and x is in the first quadrant, what is cos(x)?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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