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

a. 3x+5
b.x+5
c.2x+10
d.2x2^+5

1 answer

To find \( f(f+g)(x) \) with the given functions \( f(x) = x + 5 \) and \( g(x) = 2 \), let's first compute \( f + g \).

  1. Calculate \( f(x) + g(x) \): \[ f(x) + g(x) = (x + 5) + 2 = x + 7 \]

  2. Now calculate \( f(f + g)(x) \) by substituting \( f + g \) into \( f \): \[ f(f + g)(x) = f(x + 7) \]

  3. Now substitute \( x + 7 \) into \( f(x) = x + 5 \): \[ f(x + 7) = (x + 7) + 5 = x + 12 \]

Thus, we have \( f(f + g)(x) = x + 12 \).

It seems this result does not match any of the answer choices. There may be a misinterpretation of the original question's intention, but based on the computations, it's \( x + 12 \).

If you need any specific explanation or further assistance, let me know!