Questions: Choose f(g(x)). f(x)=3x-2; g(x)=x+3 3x+7 7x-3 3x-7 7x+3

Choose f(g(x)). f(x)=3x-2; g(x)=x+3 3x+7 7x-3 3x-7 7x+3
Transcript text: 11) Choose $f(g(x))$. \[ f(x)=3 x-2 ; g(x)=x+3 \] $3 x+7$ $7 x-3$ $3 x-7$ $7 x+3$
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Solution

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Solution Steps

To find \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). First, determine \( g(x) \), which is given as \( x + 3 \). Then, substitute \( x + 3 \) into the function \( f(x) = 3x - 2 \). This will give us the expression for \( f(g(x)) \).

Step 1: Define the Functions

We are given two functions: \[ f(x) = 3x - 2 \] \[ g(x) = x + 3 \]

Step 2: Substitute \( g(x) \) into \( f(x) \)

To find \( f(g(x)) \), we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(x + 3) \]

Step 3: Calculate \( f(g(x)) \)

Now, we substitute \( x + 3 \) into the function \( f(x) \): \[ f(g(x)) = f(x + 3) = 3(x + 3) - 2 \] Expanding this expression: \[ = 3x + 9 - 2 = 3x + 7 \]

Final Answer

The expression for \( f(g(x)) \) is: \[ \boxed{3x + 7} \]

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