Questions: Given (f(x)=4x+5) and (g(x)=x^2+7x). Find ((f circ g)(7)=)

Given (f(x)=4x+5) and (g(x)=x^2+7x). Find ((f circ g)(7)=)
Transcript text: Given $f(x)=4 x+5$ and $g(x)=x^{2}+7 x$. Find $(f \circ g)(7)=$ $\square$
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Solution

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Solution Steps

To solve the problem, we need to find the composition of the functions \( f \) and \( g \) evaluated at \( x = 7 \). This means we first evaluate \( g(7) \) and then use that result as the input for \( f \).

  1. Evaluate \( g(7) \).
  2. Use the result from step 1 as the input for \( f \).
Step 1: Evaluate \( g(7) \)

To find \( g(7) \), we substitute \( x = 7 \) into the function \( g(x) = x^2 + 7x \):

\[ g(7) = 7^2 + 7 \cdot 7 = 49 + 49 = 98 \]

Step 2: Evaluate \( f(g(7)) \)

Next, we use the result from Step 1 as the input for the function \( f(x) = 4x + 5 \):

\[ f(g(7)) = f(98) = 4 \cdot 98 + 5 = 392 + 5 = 397 \]

Final Answer

The value of \( (f \circ g)(7) \) is \\(\boxed{397}\\).

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