What is composition of functions?

Composition of functions is applying one function to the result of another function, denoted as $$(f \circ g)(x) = f(g(x))$$ .

Given $$f(x)=x^2$$ , is $$f^{-1}(x)$$ a function?

No, because it does not pass the vertical line test; the inverse is not a function.

What is the domain of the inverse function?

The domain of the inverse function is the range of the original function.

What is the range of the function $$f(x)=3x-4$$ ?

The range is all real numbers, as it is a linear function.

How do you determine if two functions are inverses?

Two functions $$f(x)$$ and $$g(x)$$ are inverses if $$f(g(x))=x$$ and $$g(f(x))=x$$ for all $$x$$ in the domain.

What is the graphical representation of inverse functions?

The graph of an inverse function is a reflection of the original function across the line $$y=x$$ .

Inverse and Composition of Functions

Flashcard

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Mathematics

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10th - 12th Grade

•

Practice Problem

•

Hard

•

CCSS

HSF-BF.B.4A, HSF-BF.A.1C, HSF-BF.B.4C

Standards-aligned

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15 questions

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FLASHCARD QUESTION

Front

The inverse of a function is the set of all ordered pairs___________or_________.

Back

(y,x) or (f(x), x)

Tags

CCSS.HSF-BF.B.4C

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.A.1C

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.A.1C

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSF-BF.A.1C

FLASHCARD QUESTION

Front

What is the definition of an inverse function?

Back

Tags

CCSS.HSF-BF.B.4A

FLASHCARD QUESTION

Front

How do you find the inverse of a linear function?

Back

Tags

CCSS.HSF-BF.B.4A

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