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Questions and Answers
What is the result of the function addition $f + g$ if $f(x) = x^3 + 2x^2$ and $g(x) = 3x^2 - 1$?
What is the result of the function addition $f + g$ if $f(x) = x^3 + 2x^2$ and $g(x) = 3x^2 - 1$?
- $x^3 + 2x^2 - 3$
- $x^3 + 5x^2 + 1$
- $x^3 + 5x^2 - 1$
- $x^3 + 2x^2 + 3x^2 - 1$ (correct)
What is $g ext{o} f$ for the functions $f(x) = x$ and $g(x) = x^3 + 2x$?
What is $g ext{o} f$ for the functions $f(x) = x$ and $g(x) = x^3 + 2x$?
- $g(f(x)) = x^3 + 2x$ (correct)
- $g(f(x)) = x + 2x$
- $f(g(x)) = x^3 + 2x$
- $f(g(x)) = x^3 + 2$
Which of the following represents the correct inverse function, $f^{-1}(x)$, for $f(x) = 5(4x - 3)/(x + 2)$?
Which of the following represents the correct inverse function, $f^{-1}(x)$, for $f(x) = 5(4x - 3)/(x + 2)$?
- $f^{-1}(x) = (x - 2)/(5(4 - x))$ (correct)
- $f^{-1}(x) = (x + 2)/(20 + x)$
- $f^{-1}(x) = (x - 2)/20 + 3$
- $f^{-1}(x) = (x + 2)/5(4x + 3)$
Determine whether the function $f(x) = 3x - rac{ ext{sqrt}(2)}{x^3}$ is odd, even, or neither.
Determine whether the function $f(x) = 3x - rac{ ext{sqrt}(2)}{x^3}$ is odd, even, or neither.
What is the composition $f ext{o} g$ if $f(x) = x^2 + 2x$ and $g(x) = x - 1$?
What is the composition $f ext{o} g$ if $f(x) = x^2 + 2x$ and $g(x) = x - 1$?
If $f(x) = x+4$ and $g(x) = 2 - 11x$, what does $f ext{o} g ext{o} h$ yield given $h(x) = x$?
If $f(x) = x+4$ and $g(x) = 2 - 11x$, what does $f ext{o} g ext{o} h$ yield given $h(x) = x$?
How would you classify the function $f(x) = 2x^2 + x - 4$ in terms of oddness or evenness?
How would you classify the function $f(x) = 2x^2 + x - 4$ in terms of oddness or evenness?
What is the composition $g ext{o} f$ if $f(x) = x^2 - 1$ and $g(x) = rac{8}{x}$?
What is the composition $g ext{o} f$ if $f(x) = x^2 - 1$ and $g(x) = rac{8}{x}$?
Flashcards
Function Composition (f∘g)
Function Composition (f∘g)
Applying function g first, then applying function f to the result.
Inverse Function
Inverse Function
A function that reverses another function's action, undoing the transformation.
Even Function
Even Function
A function where f(-x) = f(x) for all x in its domain. Its graph is symmetrical about the y-axis.
Odd Function
Odd Function
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Function Sum (f+g)
Function Sum (f+g)
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Function Difference (f−g)
Function Difference (f−g)
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f(g(x))
f(g(x))
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Vertical Line Test
Vertical Line Test
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Study Notes
Tutorial 3: Functions
- Question 1 (a): Find f+g, f-g, fog, and gof, given f(x) = x³ + 2x² and g(x) = 3x² - 1.
- Question 1 (b): Find f+g, f-g, fog, and gof, given f(x) = 1/x and g(x) = x³ + 2x.
- Question 2 (a): Find the composition of f(x) = x² + 2x and g(x) = x−1, namely fog and gof.
- Question 2 (b): Find the composition of f(x) = x + 4, g(x) = 2 - 11x, and h(x)= 1/x, namely fog.h, gof.h, and hof.g.
- Question 3: Find the inverse function for given functions:
- f(x) = 5/ (4x -3)
- f(x) = (x+2)/(x +1), x≠-1
- f(x) = 2/5 x +32/5
- f(x) = x² − 1, x ≥ 0
- f(x) = x +1
- f(x) = √(x + 1)
- f(x) = 1/(x - 3)
- f(x) = (x - 3)², x ≥ 3
- Question 4: Determine whether the following functions are odd, even, or neither:
- f(x) = 3x - √2
- g(x) = 3x² + 2x – 1
- g(x) = x³/8
- f(x) = x² + x³
- f(x) = 2x² + x − 4
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Description
This quiz covers various operations and properties of functions, including function addition, composition, and finding inverse functions. Questions include determining whether functions are odd or even and involve multiple examples for practice. Master these concepts to enhance your understanding of mathematical functions.
