What is the formula for dividing two functions?

The quotient of two functions $$f(x)$$ and $$g(x)$$ is given by $$\frac{f}{g}(x) = \frac{f(x)}{g(x)}$$ , provided @@g(x) eq 0@@.

How do you find the value of $$(f ullet g)(x)$$ for $$f(x) = 3x + 2$$ and $$g(x) = x - 5$$ ?

$$(f ullet g)(x) = f(g(x)) = f(x - 5) = 3(x - 5) + 2 = 3x - 15 + 2 = 3x - 13$$ .

What is the result of $$(f ullet g)(x)$$ if $$f(x) = 3x - 1$$ and $$g(x) = x^2 + 2$$ ?

$$(f ullet g)(x) = f(g(x)) = f(x^2 + 2) = 3(x^2 + 2) - 1 = 3x^2 + 6 - 1 = 3x^2 + 5$$ .

What is the result of $$(f / g)(a)$$ if $$f(a) = 3a + 7$$ and $$g(a) = 4a^2 - 8$$ ?

$$(f / g)(a) = \frac{f(a)}{g(a)} = \frac{3a + 7}{4a^2 - 8}$$ .

What is the result of $$(f - g)(t)$$ if $$f(t) = 3t + 2$$ and $$g(t) = t^2 - 5$$ ?

$$(f - g)(t) = f(t) - g(t) = (3t + 2) - (t^2 - 5) = -t^2 + 3t + 7$$ .

What is the domain of a function?

The domain of a function is the set of all possible input values (x-values) for which the function is defined.

What is the range of a function?

The range of a function is the set of all possible output values (y-values) that the function can produce.

Function Operations Flashcards

Student preview

14 questions

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1.

FLASHCARD QUESTION

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input from a set of inputs.

Tags

CCSS.8.F.A.1

2.

FLASHCARD QUESTION

Front

Define the term 'inverse function'.

Back

Tags

CCSS.HSF-BF.B.4A

3.

FLASHCARD QUESTION

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function, swap the x and y variables and solve for y.

Tags

CCSS.HSF-BF.B.4A

4.

FLASHCARD QUESTION

Front

What is function composition?

Back

Tags

CCSS.HSF-BF.A.1C

5.

FLASHCARD QUESTION

Front

What is the formula for adding two functions?

Back

Tags

CCSS.HSF-BF.A.1B

6.

FLASHCARD QUESTION

Front

What is the formula for subtracting two functions?

Back

Tags

CCSS.HSF-BF.A.1B

7.

FLASHCARD QUESTION

Front

What is the formula for multiplying two functions?

Back

Tags

CCSS.HSF-BF.A.1B

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