Topic Details (Notes format)

How to Find Inverse Functions

Subject: Mathematics

Book: Maths Mastery

An inverse function f⁻¹ swaps inputs and outputs of f: if y=f(x), then x=f⁻¹(y). Graphically, it reflects f across the line y=x. To find an inverse, replace f(x) with y, then solve for x in terms of y, and rename x as f⁻¹(y). For instance, y=2x+3 → x=(y–3)/2 → f⁻¹(x)= (x–3)/2. Inverse functions are crucial in algebraic transformations, “undoing” processes (like logs vs. exponentials), or solving equations about rates/time. Checking domain/range restrictions ensures the inverse is valid, reinforcing your function-centric problem-solving repertoire.

Practice Questions

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How many diagonals does a pentagon have?

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The area of an equilateral triangle with side length 6 cm is:

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If the sum of three consecutive integers is 72, what are the integers?

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The sides of a triangle are 5 cm, 12 cm, and 13 cm. What type of triangle is it?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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What is the remainder when 5^100 is divided by 3?

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If a = 4 and b = 5, what is the value of (a+b)^2?

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