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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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