Question 692·Easy·Algebra

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The function $g$ is defined by $g(x) = 5x - 7$ . If $g(x) = 18$ , what is the value of $x$ ?

A function takes an input and gives an output. Here the output is given, but the input is missing. Set the rule equal to the given output, then solve for the input. In Desmos, define the function and use a regression to find it. Don't treat the given output as the input.

Hints

Hint 1
The number after the equals sign in $g(x)=18$ is the output. The unknown input is $x$ . What equation do you get when you replace $g(x)$ with its rule?
Hint 2
A regression finds a value that makes two expressions match. Define $g$ in Desmos, then use $g(x_1)\sim18$ . Desmos treats $x_1$ as the unknown input.

Step-by-step

Set the rule equal to the output
Step 1
Turn the output into an equation
The problem gives the output $g(x)=18$ , not an input of $18$ . Since $g(x)$ means $5x-7$ , set the rule equal to the given output to find the input: $5x-7=18$ .
Step 2
Find the input in Desmos
Type $g(x)=5x-7$ , then $g(x_1)\sim18$ . The $\sim$ tells Desmos to find an unknown input; an ordinary $x$ would be graphed instead. Under PARAMETERS, Desmos shows $x_1=5$ . So the value of $x$ that gives an output of $18$ is $5$ . Choice B.

Question 692·Easy·Algebra

Strategy

Hints

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Strategy

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