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Chapter 1: Problem 59

Graph the function and determine the interval(s) for which \(f(x) \geq 0\). $$f(x)=\sqrt{x-1}$$

Short Answer

Expert verified
The function \(f(x) = \sqrt{x-1}\) is greater than or equal to 0 for the interval \(x \geq 1\).

Step by step solution

01

Analyze the function

The function \(f(x)=\sqrt{x-1}\) features a square root. Square roots always return positive values or zero (for \(x = 0\)). It's also known that the function is undefined for values where \(x-1<0\), i.e. \(x<1\).
02

Graph the function

Plotting the function, one can observe that the graph starts from the point (1,0), and goes upwards as \(x\) increases. The function is not defined for \(x<1\), therefore there is no graph to the left of the \(y\)-axis.
03

Determine the interval where the function is greater than or equal to zero

From Step 1, we know that the function's value is always greater than or equal to zero (provided \(x\) is greater than or equal to 1), and from the graph in Step 2, we see that this is indeed the case. Therefore, the function \(f(x)\) is greater than or equal to 0 for all \(x\) where \(x \geq 1\).

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