Operations & Compositions & Inverses

Flashcard
•
Mathematics
•
9th Grade
•
Hard
+4
Standards-aligned
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15 questions
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1.
FLASHCARD QUESTION
Front
What are inverse functions?
Back
Inverse functions are functions that reverse the effect of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y and produces the original input x.
Tags
CCSS.HSF-BF.B.4A
2.
FLASHCARD QUESTION
Front
How can you determine if two functions are inverses of each other?
Back
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 of both functions.
Tags
CCSS.HSF-BF.B.4B
3.
FLASHCARD QUESTION
Front
What is the significance of the line y = x in relation to inverse functions?
Back
The line y = x is the line of reflection for inverse functions. The graph of a function and its inverse are symmetric with respect to this line.
Tags
CCSS.HSF-BF.B.4C
4.
FLASHCARD QUESTION
Front
What is function composition?
Back
Function composition is the process of applying one function to the results of another function. If f and g are functions, the composition is denoted as (f ∘ g)(x) = f(g(x)).
Tags
CCSS.HSF-BF.A.1C
5.
FLASHCARD QUESTION
Front
Given p(x) = 3x + 4 and q(x) = 2x², how do you find p(q(x))?
Back
To find p(q(x)), substitute q(x) into p(x): p(q(x)) = p(2x²) = 3(2x²) + 4 = 6x² + 4.
Tags
CCSS.HSF-BF.A.1C
6.
FLASHCARD QUESTION
Front
What is the formula for the sum of two functions f(x) and g(x)?
Back
The sum of two functions is given by (f + g)(x) = f(x) + g(x).
Tags
CCSS.HSF-BF.A.1B
7.
FLASHCARD QUESTION
Front
How do you find the value of f(g(a))?
Back
To find f(g(a)), first evaluate g(a) to get a value, then substitute that value into f(x).
Tags
CCSS.HSF-BF.A.1C
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