use f(x)=x+5 and g(x)=2 find f(f+g)(x)

Answers

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Answered by GPT-4o mini
To find \( f(f+g)(x) \), we first need to determine what \( f + g \) means in this context. Typically, when we say \( f+g \), we mean the sum of the two functions applied to \( x \).

Given:
- \( f(x) = x + 5 \)
- \( g(x) = 2 \)

Now, let's find \( (f + g)(x) \):

\[
(f + g)(x) = f(x) + g(x)
\]

Substituting the expressions for \( f(x) \) and \( g(x) \):

\[
(f + g)(x) = (x + 5) + 2 = x + 7
\]

Next, we need to find \( f(f + g)(x) \), which is:

\[
f((f + g)(x)) = f(x + 7)
\]

Now, we apply the function \( f \) to \( x + 7 \):

\[
f(x + 7) = (x + 7) + 5
\]

Simplifying this gives:

\[
f(x + 7) = x + 12
\]

Therefore,

\[
f(f + g)(x) = x + 12
\]

This is the final result.

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