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Given \( f(x)=3 x+4 \) and \( g(x)=3 x+5 \), what is \( f(g(x)) \) ? 9x+19 \( 9 x-19 \) -9x+11 \( 9 x-11 \)

Ask by Lee Gray. in the Philippines
Dec 07,2024

Real Tutor Solution

Tutor-Verified Answer

Answer

\( f(g(x)) = 9x + 19 \)

Solution

To find \( f(g(x)) \), we need to substitute \( g(x) \) into \( f(x) \). Given: \[ f(x) = 3x + 4 \] \[ g(x) = 3x + 5 \] Now, we substitute \( g(x) \) into \( f(x) \): \[ f(g(x)) = f(3x + 5) \] Now, we replace \( x \) in \( f(x) \) with \( 3x + 5 \): \[ f(3x + 5) = 3(3x + 5) + 4 \] Now, we distribute the 3: \[ = 9x + 15 + 4 \] Now, we combine the constants: \[ = 9x + 19 \] Thus, the result is: \[ f(g(x)) = 9x + 19 \] The correct answer is \( 9x + 19 \).

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Extra Insights

To find \( f(g(x)) \), we first need to plug \( g(x) \) into \( f(x) \). Since \( g(x) = 3x + 5 \), we substitute this into \( f(x) = 3x + 4 \): \[ f(g(x)) = f(3x + 5) = 3(3x + 5) + 4 \] Now, simplify this: \[ f(g(x)) = 9x + 15 + 4 = 9x + 19 \] Therefore, \( f(g(x)) = 9x + 19 \). So, the answer is \( 9x + 19 \).

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