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

The simple interest on Rs. 4000 at 5% per annum for 2 years is:

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A train 120 meters long is moving at a speed of 54 km/h. How long will it take to pass a pole?

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If two complementary angles differ by 30°, what are the angles?

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What is the sum of the interior angles of a hexagon?

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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 the first 50 positive integers?

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The sides of a triangle are 7, 24, and 25. Is this a right triangle?

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

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If sin(A) = 1/2 and A is acute, what is the value of A?

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