Podcast
Questions and Answers
If $f(x) = 3x + 5$, what is $f(0)$?
If $f(x) = 3x + 5$, what is $f(0)$?
5
If $g(x) = \frac{2x + 9}{4}$, what is $g(0)$?
If $g(x) = \frac{2x + 9}{4}$, what is $g(0)$?
9/4
If $h(x) = x^2 - 5$, what is $h(7)$?
If $h(x) = x^2 - 5$, what is $h(7)$?
44
If $f(x) = 3x - 8$, solve for $x$ when $f(x) = 7$.
If $f(x) = 3x - 8$, solve for $x$ when $f(x) = 7$.
If $g(x) = 19 - 4x$, solve for x when $g(x) = 31$.
If $g(x) = 19 - 4x$, solve for x when $g(x) = 31$.
If $h(x) = \frac{5x - 1}{2}$, solve for $x$ when $h(x) = 32$.
If $h(x) = \frac{5x - 1}{2}$, solve for $x$ when $h(x) = 32$.
If $f(x) = x^2 - 2x + 3$, solve for $x$ when $f(x) = 27$.
If $f(x) = x^2 - 2x + 3$, solve for $x$ when $f(x) = 27$.
If $f(x) = x + 5$ and $g(x) = 3x - 1$, what is the value of $g(1)$?
If $f(x) = x + 5$ and $g(x) = 3x - 1$, what is the value of $g(1)$?
If $g(x) = 3x - 8$, what is $g(-2)$?
If $g(x) = 3x - 8$, what is $g(-2)$?
If $f(x) = \frac{32}{x^2}$, what is $f(4)$?
If $f(x) = \frac{32}{x^2}$, what is $f(4)$?
If $g(x) = 2x^3$, what is $g(1)$?
If $g(x) = 2x^3$, what is $g(1)$?
If $f(x) = 2x + 1$ and $g(x) = x - 5$, what is $g(x)$?
If $f(x) = 2x + 1$ and $g(x) = x - 5$, what is $g(x)$?
If $h(x) = x^2$, what is $h(x)$?
If $h(x) = x^2$, what is $h(x)$?
If $f(x) = 2x$, what is $f^{-1}(x)$?
If $f(x) = 2x$, what is $f^{-1}(x)$?
If $f(x) = x - 6$, what is $f^{-1}(x)$?
If $f(x) = x - 6$, what is $f^{-1}(x)$?
If $h(x) = \frac{x}{4}$, what is $h^{-1}(x)$?
If $h(x) = \frac{x}{4}$, what is $h^{-1}(x)$?
Flashcards
What is a function?
What is a function?
A mathematical rule that assigns each input value to a single output value.
What is evaluating a function?
What is evaluating a function?
Substituting a given value into a function and calculating the result.
What is substitution in functions?
What is substitution in functions?
Replacing the variable 'x' in the function's expression with the specified value.
What does 'Solve f(x) = a' mean?
What does 'Solve f(x) = a' mean?
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What is composite function?
What is composite function?
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What is an inverse function?
What is an inverse function?
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What is function composition?
What is function composition?
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What does solve f(a) = g(a) mean?
What does solve f(a) = g(a) mean?
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Study Notes
- Functions are covered in Corbettmaths videos 369 and 370.
Function Evaluation
- To evaluate a function f(x) at a specific value, substitute that value for x in the function's expression.
- For a function g(x), g(a) means replacing x with a in the expression defining g.
- When given f(x) = some expression, solving f(x) = a constant involves finding the x value that makes the function equal to that constant.
- Composite functions, like fg(x), involve substituting the function g(x) into the function f(x).
- The inverse of h(x) is denoted as h⁻¹(x).
- To find a value "a" such that f(a) = g(a), set the expressions for f(x) and g(x) equal to each other and solve for x.
- To express a function in the form ax² + bx + c, expand and simplify the expression for the function.
- For functions f(x) and g(x), solving fg(x) = gf(x) involves finding the x values for which the composite functions are equal.
- To show that f(x + 1) - f(x) = some expression, substitute (x + 1) into f(x), subtract f(x), and simplify to match the given expression.
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