Final answer:
To find g(f(2)), we first calculate f(2) by using the value of z from the equation 13z = 2.78, followed by substituting the result into g(x). After performing the calculations, we find that g(f(2)) is approximately 0.9714.
Step-by-step explanation:
To find g(f(2)), we first calculate f(2) by using the value of z from the equation 13z = 2.78, followed by substituting the result into g(x). After performing the calculations, we find that g(f(2)) is approximately 0.9714.
To find g(f(2)), we need to first evaluate f(2). Given that f(x) = 1/3 - z, we substitute x with 2 and use the provided equation 13z = 2.78 to find the value of z. Solving for z gives us z = 2.78 / 13, which is approximately z ≈ 0.2138. Inserting this into the function f(x) yields f(2) = 1/3 - 0.2138 ≈ 0.1195.
Next, we evaluate g(f(2)), which means we need to substitute the result from f(2) into g(x). With g(x) = 1 - 2x^2, we calculate g(0.1195) ≈ 1 - 2(0.1195)^2 ≈ 1 - 2(0.01428025) ≈ 1 - 0.0285605 ≈ 0.9714395.
Therefore, g(f(2)) ≈ 0.9714.