Find the Roots (Zeros) f(x) = square root of 9-x^2

Problem

ƒ(x)=√(,9−x2)

Solution

1. Set the function to zero to find the roots, as roots occur where the output of the function is zero.

ƒ(x)=0

2. Substitute the expression for ƒ(x) into the equation.

√(,9−x2)=0

3. Square both sides of the equation to eliminate the square root.

9−x2=0

4. Isolate the variable by adding x2 to both sides.

9=x2

5. Solve for x by taking the square root of both sides, remembering to include both the positive and negative results.

x=±√(,9)

6. Simplify the result to find the specific values of x

x=±3

Final Answer

√(,9−x2)=0⇒x=3,−3

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