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Let f:R→R, g:R→R be two functions given...

Let `f:R→R, g:R→R` be two functions given by`f(x)=2x+4`,`g(x)=x-4` then `fog(x)` is

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To find \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). ### Step-by-Step Solution: 1. **Identify the Functions**: We have two functions: \[ f(x) = 2x + 4 \] \[ g(x) = x - 4 \] 2. **Find \( g(x) \)**: We know that: \[ g(x) = x - 4 \] 3. **Substitute \( g(x) \) into \( f(x) \)**: We need to find \( f(g(x)) \), which means we will replace \( x \) in \( f(x) \) with \( g(x) \): \[ f(g(x)) = f(x - 4) \] 4. **Calculate \( f(x - 4) \)**: Now, substitute \( x - 4 \) into the function \( f(x) \): \[ f(x - 4) = 2(x - 4) + 4 \] 5. **Simplify the Expression**: Distributing the \( 2 \): \[ = 2x - 8 + 4 \] Combine like terms: \[ = 2x - 4 \] 6. **Final Result**: Thus, we have: \[ f(g(x)) = 2x - 4 \] ### Summary: The composition of the functions \( f(g(x)) \) results in: \[ f(g(x)) = 2x - 4 \]
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