Podcast
Questions and Answers
If $f(x) = x - 4$, what is the value of $f(5)$?
If $f(x) = x - 4$, what is the value of $f(5)$?
- -1
- 1 (correct)
- -9
- 9
Given $g(x) = 2x^2 - 10$, what is the value of $g(2)$?
Given $g(x) = 2x^2 - 10$, what is the value of $g(2)$?
- -8
- 2
- 8
- -2 (correct)
Given $f(x) = x^2 - 3$, what is the value of $f(10)$?
Given $f(x) = x^2 - 3$, what is the value of $f(10)$?
- -7
- 103
- 97 (correct)
- 7
If $f(x) = 2x - 4$ and $g(x) = 3x + 5$, what is the value of $f(3)$?
If $f(x) = 2x - 4$ and $g(x) = 3x + 5$, what is the value of $f(3)$?
Given $f(x) = 3x + 1$ and $g(x) = x^2$, what is $g(x)$?
Given $f(x) = 3x + 1$ and $g(x) = x^2$, what is $g(x)$?
If $f(x) = x^2 - 17$ and $g(x) = x + 3$, what is $g(x)$?
If $f(x) = x^2 - 17$ and $g(x) = x + 3$, what is $g(x)$?
A function $f$ is defined such that $f(x) = x^2 - 1$. What is the value of $f(x)$ when $x = 0$?
A function $f$ is defined such that $f(x) = x^2 - 1$. What is the value of $f(x)$ when $x = 0$?
A function $f$ is defined such that $f(x) = 4x - 1$. What is the value of $f(0)$?
A function $f$ is defined such that $f(x) = 4x - 1$. What is the value of $f(0)$?
If $g(x) = kx^2$, what is the value of $g(2)$?
If $g(x) = kx^2$, what is the value of $g(2)$?
Flashcards
What does f(x) mean?
What does f(x) mean?
f(x) means 'apply the function f to x'. Substitute the value inside the parentheses into the function.
What is an inverse function?
What is an inverse function?
Given a function f(x), the inverse function, denoted f⁻¹(x), 'undoes' the operation of f(x). If f(a) = b, then f⁻¹(b) = a.
What is a composite function?
What is a composite function?
A composite function applies one function to the result of another. f(g(x)) means apply g to x, then apply f to the result.
How to calculate g(f(x))?
How to calculate g(f(x))?
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How do you find the inverse function?
How do you find the inverse function?
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fg(x)
fg(x)
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Study Notes
- These notes cover compound and inverse functions
Question 1
- Given f(x) = x - 4, f(5) = 5 - 4 = 1
- Given f(x) = x - 4, f(3) = 3 - 4 = -1
Question 2
- Given g(x) = 2x² - 10, g(2) = 2(2²) - 10 = -2
- Given g(x) = 2x² - 10, g(-2) = 2(-2)² - 10 = -2
- To solve g(x) = 8, set 2x² - 10 = 8, which simplifies to x² = 9, therefore x = 3
Question 3
- Given f(x) = 3x - 5, f(3) = 3(3) - 5 = 4
- Given f(x) = 3x - 5, f(-2) = 3(-2) - 5 = -11
- To solve f(x) = 1, set 3x - 5 = 1, which simplifies to x = 2
Question 4
- Given f(x) = x² - 3, f(10) = 10² - 3 = 97
- Given f(x) = x² - 3, f(-1) = (-1)² - 3 = -2
- The inverse function f⁻¹(x) = √(x + 3)
Question 5
- Given f(x) = 2x - 4 and g(x) = 3x + 5, to find gf(3) you need to calculate f(3) and then substitue it into g(x)
- An expression for f⁻¹(x) becomes f⁻¹(x) = (x + 4) / 2
- To solve f(x) = g(x), set 2x - 4 = 3x + 5, which simplifies to x = -9
Question 6
- Given f(x) = 3x + 1 and g(x) = x², fg(x) = 3x² + 1
- Given f(x) = 3x + 1 and g(x) = x², gf(x) = (3x + 1)²
- To solve fg(x) = gf(x), set 3x² + 1 = (3x + 1)², which simplifies to 6x² + 6x = 0
Question 7
- Given f(x) = x² - 17 and g(x) = x + 3, determine the expressions for the inverse functions to then solve
Question 8
- Given f(x) = x² - 1, determine the expression of f(x-2) and then solve
Question 9
- Given f(x) = 4x - 1, determine the inverse function: f⁻¹(x)
- Given g(x) = kx² and fg(2) = 12, where is a constant, determine k
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