Inverse Functions (AQA A-Level Mathematics): Quizzes

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Inverse Functions
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What condition must a function satisfy to have an inverse?

It must be one-to-one

Why does f(x)=x2,x∈Rf(x) = x^2, x \in \mathbb{R} have no inverse?

It is many-to-one

How can we make f(x)=x2f(x) = x^2 have an inverse?

Restrict the domain to x≥0x \geq 0

What is f−1(x)f^{-1}(x) for f(x)=x2,x≥0f(x) = x^2, x \geq 0?

x\sqrt{x}

What is the first step in finding the inverse of a function?

Write as y=f(x)y = f(x) and swap xx and yy

The domain of f−1(x)f^{-1}(x) equals what property of f(x)f(x)?

The range of f(x)f(x)

What is f−1(x)f^{-1}(x) for f(x)=ex,x∈Rf(x) = e^x, x \in \mathbb{R}?

ln⁡(x),x>0\ln(x), x > 0

For f(x)=2x+3,x>3f(x) = 2x + 3, x > 3, what is f−1(x)f^{-1}(x)?

x−32,x≥9\frac{x-3}{2}, x \geq 9

How is the graph of f−1(x)f^{-1}(x) related to the graph of f(x)f(x)?

Reflection through line y=xy = x

Where do y=f(x)y = f(x) and y=f−1(x)y = f^{-1}(x) intersect?

On the line y=xy = x

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