Question 88·Easy·Linear Functions
The function is defined by . If , what is the value of ?
For function questions like this, first rewrite the situation as an equation: set the given function expression equal to the output value (here, ). Then solve the resulting one-step-or-two-step linear equation by systematically undoing operations in reverse order—first move constants (like ), then divide by the coefficient of . Check quickly by plugging your value of back into the original function to ensure it produces the given output.
Hints
Write the equation you need to solve
Replace with and set it equal to 18. What equation in terms of do you get?
Isolate the x-term
Your equation should look like . What operation will undo the on the left side?
Finish solving for x
After you move the to the other side, you will have equal to some number. What do you do to both sides to get alone?
Desmos Guide
Use Desmos to compute x directly
In a new expression line, type (18 + 7) / 5 (this comes from solving by adding 7 to both sides, then dividing by 5). Look at the numerical result Desmos shows; that value is the that makes .
Step-by-step Explanation
Translate the function statement into an equation
You are told and that .
Set these equal to each other:
Now you just need to solve this linear equation for .
Undo the subtraction to isolate the term with x
To move the to the other side, add 7 to both sides of the equation:
Now the equation is simpler: .
Solve for x
To solve , divide both sides by 5:
So, the value of is 5, which corresponds to choice B.