Language of Functions (Edexcel A-Level Mathematics): Flashcards

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Language of Functions
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What does f:x→x2+2f: x \rightarrow x^2 + 2 mean?

It means f(x)=x2+2f(x) = x^2 + 2 for all xx.

What is the domain of a function?

The set of xx values allowed to be input in a function.

What is the range of a function?

The set of yy values that f(x)f(x) can take for a domain.

What is the domain of f(x)=2x+3f(x) = 2x + 3 for x>3x > 3?

The domain is {x:x>3}\{x: x > 3\}.

How is an incorrect domain defined?

A domain where the function is undefined for some xx values.

Find the range of g(x)=exg(x) = e^x for x≥2x \geq 2.

Range is {y:y≥e2}\{y: y \geq e^2\}.

What is the range of f(x)=2−xf(x) = 2 - \sqrt{x} for x≥0x \geq 0?

Range is (−∞,2](-\infty, 2] as xx goes from 00 to ∞\infty.

What defines a many-to-one function in mathematics?

Multiple xx values map to a single yy value.

What indicates a many-to-many function?

One xx value gives multiple yy values, no inverse exists.

Define the notation for real numbers.

R={real numbers}\mathbb{R} = \{\text{real numbers}\}.

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