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Chapter 2: Problem 117

Determine (if possible) the zeros of the function \(g\) when the function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\) $$g(x)=-f(x)$$

Short Answer

Expert verified
The zeros of the function \(g(x) = -f(x)\) are the same as the zeros of the function \(f(x)\), which are \(x = r_1, r_2, r_3\).

Step by step solution

01

Understanding the Function

First, the function \(g(x) = -f(x)\) is the negative of the function \(f(x)\). This means that the values of \(f(x)\) are multiplied by -1 to give the values of \(g(x)\).
02

Finding the Zeros

Next, you determine the zeros of \(g(x)\), the x-values where \(g(x) = 0\). Since \(g(x) = -f(x)\), and we know that \(x = r_1, r_2, r_3\) are the zeros of \(f(x)\) (as \(f(r_1) = f(r_2) = f(r_3) = 0\)), we then have \(g(r_1) = g(r_2) = g(r_3) = 0\).
03

Conclusion

Consequently, the zeros of the function \(g(x) = -f(x)\) are the same as the zeros of \(f(x)\), i.e., at \(x = r_1, r_2, r_3\).

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Most popular questions from this chapter

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