Question 302·Easy·Algebra

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The linear function $g$ is defined by $g(x)=5x-7$ . For what value of $x$ does $g(x)=18$ ?

A function turns an input into an output. The cue here is a given output with the input missing: set the rule equal to the output to find the input. In Desmos, define the function and use a regression to find that input. Don’t mistake the given output for the input.

Hints

Hint 1
The number in $g(x)=18$ is the output, not the input. You need the missing input $x$ . What equation do you get when you replace $g(x)$ with its rule?
Hint 2
A regression asks Desmos to find a value that makes two sides equal. Use $x_1$ for the unknown input and $\sim$ in place of $=$ . What should $g(x_1)$ equal?

Step-by-step

Find the input with Desmos
Step 1
Turn the given output into an equation
$g(x)$ is the output for input $x$ . The problem gives the output $g(x)=18$ , so replace $g(x)$ with its rule:
$5x-7=18$
The $18$ belongs on the output side; it isn’t a number to put in for $x$ .
Step 2
Find the input that produces 18
Type $g(x)=5x-7$ , then $g(x_1)\sim18$ . Desmos uses $x$ for graphing, so $x_1$ stands for the unknown input. The regression symbol $\sim$ tells Desmos to find a value that makes both sides equal. Under PARAMETERS, it reports $x_1=5$ . So the input that gives $g(x)=18$ is $5$ . Choice B.

Question 302·Easy·Algebra

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Strategy

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