Answer:
a) f(x) = 12x +11
b) f(x) = 12(x +11)
c) f(x) = x/2 -6
d) f(x) = (x -6)/2
Step-by-step explanation:
The "and then ..." operation applies to the entire result of the first operation.
a)
"multiplies input by 12" = 12x
"and then adds 11" = 12x +11
f(x) = 12x +11
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b)
"adds 11 to the input" = x +11
"and then multiplies by 12" = (x +11)×12 = 12(x +11)
f(x) = 12(x +11)
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c)
f(x) = x/2 -6
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d)
f(x) = (x -6)/2
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Additional comment
When you write division expressions in plain text using a slash (/) or "divided by" symbol (÷), you need to be careful to identify what the numerator and denominator are. If either one is other than a single token (variable or constant), then parentheses must be used to indicate what is part of the group.
In typeset text, the answer to (d) looks like ...
[tex]f(x)=\dfrac{x-6}{2}[/tex]
If you write this in plain text as ...
f(x) = x -6/2
the Order of Operations requires that you do the division first, giving 6/2 = 3, then the subtraction: x -3. Of course, this result is something entirely different from the f(x) described in part (d). In short, the fraction bar in the typeset expression serves as a grouping symbol, so (x -6) is treated as a single unit. In plain text, the only grouping symbol available is parentheses, so the expression must be written as ...
f(x) = (x -6)/2
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The same sort of logic applies to other typeset symbols that do grouping. A radical is another one of these:
[tex]g(x)=\sqrt{x-6}[/tex]
is not the same as g(x) = √x -6. However, it is the same as g(x) = √(x -6).
