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Chapter 2: Problem 118

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

Short Answer

Expert verified
The function \(g\) has zeros at \(x=r_{1}, x=r_{2}, \) and \(x=r_{3}\).

Step by step solution

01

Identify the Zeros of Function \(f\)

The given function \(f\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\). This implies that \(f(r_{1})=0\), \(f(r_{2})=0\) and \(f(r_{3})=0\).
02

Evaluate the Function \(g(x)\)

The given function \(g(x)\) is \(3 \cdot f(x)\). If we insert \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\), into the function \(g(x)\), we see that \(g(r_{1})=3f(r_{1})=3 \cdot 0 =0\), \(g(r_{2})=3f(r_{2})=3 \cdot 0 =0\) and \(g(r_{3})=3f(r_{3})=3 \cdot 0 =0\). Thus, \(g(r_{i})=0\) for all \(i=1,2,3\).
03

Identify the Zeros of Function \(g\)

The zeros of a function are the x-values that make the function equal to zero. As we found that \(g(r_{i})=0\) for all \(i=1,2,3\), we conclude that function \(g\) has zeros at \(x=r_{1}, x=r_{2},\) and \(x=r_{3}\).

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Most popular questions from this chapter

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