Final answer:
To find the expression equivalent to g(f(x)), substitute f(x) into g(x) by replacing x in g(x) with the expression for f(x). Expand the square and subtract 5 to get the equivalent expression.
Step-by-step explanation:
To find the expression equivalent to g(f(x)), we need to substitute f(x) into g(x).
The given functions are f(x) = 3x + 1 and g(x) = x^2 - 5.
To substitute f(x) into g(x), we replace x in g(x) with the expression for f(x). So, g(f(x)) becomes g(3x + 1).
Substituting the expression for f(x) into g(x), we get g(f(x)) = (3x + 1)^2 - 5.
Expanding the square, we get (3x + 1)(3x + 1) = 9x^2 + 6x + 1, and subtracting 5, we get g(f(x)) = 9x^2 + 6x - 4.
Therefore, the equivalent expression to g(f(x)) is 9x^2 + 6x - 4.