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

A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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What is the value of x if 3x + 7 = 16?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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What is the sum of all angles in a hexagon?

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If a square has a perimeter of 64 cm, what is its area?

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What is the probability of drawing an ace from a standard deck of 52 cards?

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

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If the sum of the angles of a polygon is 1080°, how many sides does the polygon have?

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What is the sum of the first 10 positive even numbers?

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

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