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Chapter 1: Problem 38

Find all real values of \(x\) such that \(f(x)=0\). $$f(x)=5 x+1$$

Short Answer

Expert verified
The real value of \(x\) that satisfies the given function \(f(x) = 5x + 1 = 0\) is \(x = -1/5\).

Step by step solution

01

Definition of the linear function

The function \(f(x)\) has been given as \(f(x) = 5x + 1\). The task is to find out the real values of \(x\) for which \(f(x) = 0\).
02

Set the function to zero

Since the aim is to find the root of the function, set \(f(x) = 0\). Hence, we get the equation as \(0 = 5x + 1\).
03

Isolate \(x\) in the equation

Solve the equation for \(x\) by subtracting 1 from both sides of the equation. So, the formula becomes \(-1 = 5x.\)
04

Solving for \(x\)

Finally, divide both sides of equation by 5 to isolate \(x\), giving \(x = -1/5\).

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