Questions: Determine f(x-1) for the following function. f(x) = sqrt(x-5) - 9

Transcript text: Determine $f(x-1)$ for the following function. \[ f(x)=\sqrt{x-5}-9 \]

Solution

Step 1: Define the Original Function

The original function is given by: \[ f(x) = \sqrt{x - 5} - 9 \]

Step 2: Substitute $x$ with $x-1$

To find $f(x-1)$, we substitute $x$ with $x-1$ in the original function: \[ f(x-1) = \sqrt{(x-1) - 5} - 9 \]

Step 3: Simplify the Expression

Simplify the expression inside the square root: \[ f(x-1) = \sqrt{x - 6} - 9 \]

\[ \boxed{f(x-1) = \sqrt{x - 6} - 9} \]

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