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find fog If the funtion f(x)=x-1 and g(x...

find `fog` If the funtion `f(x)=x-1` and `g(x)=x-3`.

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To find \( f(g(x)) \) given the functions \( f(x) = x - 1 \) and \( g(x) = x - 3 \), we will follow these steps: ### Step 1: Identify the functions We have: - \( f(x) = x - 1 \) - \( g(x) = x - 3 \) ### Step 2: Substitute \( g(x) \) into \( f(x) \) We need to find \( f(g(x)) \). This means we will substitute \( g(x) \) into the function \( f \). So, we will calculate: \[ f(g(x)) = f(x - 3) \] ### Step 3: Apply the definition of \( f \) Now, we will use the expression for \( f(x) \) to evaluate \( f(x - 3) \): \[ f(x - 3) = (x - 3) - 1 \] ### Step 4: Simplify the expression Now, we simplify the expression: \[ f(x - 3) = x - 3 - 1 = x - 4 \] ### Conclusion Thus, the final result is: \[ f(g(x)) = x - 4 \] ---
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