f of g = x⁴ + 6x² + 8
Step-by-step explanation:
f(x) = x² - 1, g(x) = x² + 3
f o g(x) means we replace the x in f(x) with the g(x) function
f o g(x) = (x² + 3)² - 1
expanding the bracket:
f o g(x) = (x² + 3)(x² + 3) - 1
= x²(x² + 3) + 3(x² + 3) - 1
= x⁴ + 3x² + 3x² + 9 - 1
collect like terms:
f o g(x) = x⁴ + 6x² + 8
Hence, f of g = x⁴ + 6x² + 8