Final answer:
To find f(x+4), substitute x+4 in place of x in f(x) and simplify.
Step-by-step explanation:
To find the expression for f(x+4), we substitute x+4 in place of x in the given expression f(x). Hence, f(x+4) = (x+4)^2 + 6(x+4) + 1.
Expanding this expression, we get f(x+4) = x^2 + 8x + 16 + 6x + 24 + 1.
Combining like terms, we simplify to f(x+4) = x^2 + 14x + 41.
Therefore, the correct answer is (a) x^2 + 14x + 49.
Then add 1 to complete the function:
f(x+4) = x^2 + 8x + 16 + 6x + 24 + 1
Combine like terms:
f(x+4) = x^2 + (8x + 6x) + (16 + 24 + 1) = x^2 + 14x + 41
However, none of the given options match this result. There may be a mistake in the options or in the process of solving the equation.