Functions (Edexcel A-Level Mathematics): Quizzes

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Inverse Functions
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What property must a function have to possess an inverse?

One-to-one

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

It is many-to-one

What is the inverse of f(x)=x2,x0f(x) = x^2, x \geq 0?

f1(x)=xf^{-1}(x) = \sqrt{x}

What is the first step to find the inverse of a function?

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

The domain of f1(x)f^{-1}(x) equals which property of f(x)f(x)?

The range of f(x)f(x)

What is the inverse of f(x)=ex,xRf(x) = e^x, x \in \mathbb{R}?

f1(x)=ln(x)f^{-1}(x) = \ln(x)

A function and its inverse are reflections through which line?

y=xy = x

If f(x)f(x) and f1(x)f^{-1}(x) intersect, where do they meet?

On the line y=xy = x

For f(x)=2x+3,x>3f(x) = 2x + 3, x > 3, find f1(x)f^{-1}(x).

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

What is the domain of f1(x)f^{-1}(x) if f(x)=2x+3,x>3f(x) = 2x + 3, x > 3?

x9x \geq 9

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