Question
Find the zero of the linear function. \( f(x)=-x+6 \)
Ask by Norris Lyons. in the United States
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The zero of the function is \( x=6 \).
Solution
Solve the equation \( -x+6=0 \).
Solve the equation by following steps:
- step0: Solve for \(x\):
\(-x+6=0\)
- step1: Move the constant to the right side:
\(-x=0-6\)
- step2: Remove 0:
\(-x=-6\)
- step3: Change the signs:
\(x=6\)
The zero of the linear function \( f(x)=-x+6 \) is \( x=6 \).
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Simplify this solution Bonus Knowledge
To find the zero of the linear function \( f(x)=-x+6 \), you need to solve for \( x \) when \( f(x) = 0 \). Setting the equation to zero gives you: \[ 0 = -x + 6 \] Now, add \( x \) to both sides: \[ x = 6 \] So, the zero of the function \( f(x) \) is \( x = 6 \). To visualize this, imagine plotting the line on a graph. It intersects the x-axis at the point (6, 0). Not only does this point represent the zero of the function, but it also signifies the equilibrium where inputs (x-values) produce an output of zero. It’s like finding the perfect balance on a seesaw!
