Question 859·Easy·Math

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The function $g$ is defined by

g(y)=\sqrt{y+9}-3.

What is the value of $g(7)$ ?

Your answer

A function evaluation asks for an output when the input is given. The number in parentheses replaces the variable in the rule, even if that variable is $y$ . Define the rule in Desmos, then evaluate it at the given input. Watch whether a number is subtracted outside the square root.

Hints

Hint 1
In function notation, the number in parentheses is the input. For $g(7)$ , replace the $y$ in the rule with $7$ .
Hint 2
The square root covers only $y+9$ . After substituting, take that square root before subtracting the number outside it.

Step-by-step

Substitute and evaluate in Desmos
Step 1
Put the input into the rule
The input in $g(7)$ is $7$ , so replacing $y$ gives $g(7)=\sqrt{7+9}-3$ . Replace the rule's variable with the number in parentheses, even when that variable is $y$ . Type $g(y)=\sqrt{y+9}-3$ into Desmos to save the given rule.
Step 2
Read the output
Type $g(7)$ on the next line. Desmos shows $1$ . It takes the square root of $7+9$ before subtracting $3$ ; stopping at the square root would leave part of the rule undone. So the value of $g(7)$ is $1$ . Grid in 1.

Question 859·Easy·Math

Strategy

Hints

Step-by-step

Lessons that teach this

Study Hints

Strategy

Hints

Step-by-step

Lessons that teach this