Answer:
(f o g)(x) = 4x⁴ - 96x + 37
(g o f)(x) = 16x⁴ + 8x² - 2
Step-by-step explanation:
Since, the given functions are,
f(x) = 4x² + 1
g(x) = x² - 3
(f o g)(x) = f[g(x)]
f[g(x)] = 4(x² - 3)² + 1
= 4(x⁴ - 24x + 9) + 1
= 4x⁴ - 96x + 36 + 1
= 4x⁴ - 96x + 37
(g o f)(x) = g[f(x)]
= (4x² + 1)²- 3
= 16x⁴ + 8x² + 1 - 3
= 16x⁴ + 8x² - 2
Therefore, out of the given options only two expressions are correct.
