Inverse functions (AQA GCSE Further Maths): Quizzes

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Inverse functions
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What does an inverse function do?

Undoes what the original function does

What is required for a function to have an inverse?

It must be one-to-one

Why does y=x2y = x^2 need a restricted domain to have an inverse?

Same output for different inputs

What is Step 2 when finding an inverse function algebraically?

Interchange x and y

What is the inverse of f(x)=2x+3f(x) = 2x + 3?

f1(x)=x32f^{-1}(x) = \frac{x - 3}{2}

A function and its inverse are reflections across which line?

y=xy = x

The domain of f(x)f(x) becomes what for f1(x)f^{-1}(x)?

The range of f1(x)f^{-1}(x)

What does the notation f1(x)f^{-1}(x) represent?

The inverse function

How can you verify you've found the correct inverse function?

Check f(f1(x))=xf(f^{-1}(x)) = x and vice versa

If point (a,b)(a, b) is on function f(x)f(x), what point is on f1(x)f^{-1}(x)?

(b,a)(b, a)

What is the inverse of f(x)=x+2f(x) = x + 2?

f1(x)=x2f^{-1}(x) = x - 2

How are quadratic functions typically restricted to have inverses?

x0x \geq 0 or x0x \leq 0

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