if f(x)=9-x^2 and g(x)=x^2+4, find (g o f)(x) and (f o g)(x)
just plug and chug:
g(x) = x²+4
g(f) = f²+4 = (9-x²)² + 4
= 81 - 18x² + x⁴ + 4
= x⁴ - 18x² + 85
f(x) = 9-x²
f(g) = 9-g² = 9-(x²+4)² = 9 - x⁴ - 8x² - 16
= -x⁴ - 8x² - 7
g(x) = x²+4
g(f) = f²+4 = (9-x²)² + 4
= 81 - 18x² + x⁴ + 4
= x⁴ - 18x² + 85
f(x) = 9-x²
f(g) = 9-g² = 9-(x²+4)² = 9 - x⁴ - 8x² - 16
= -x⁴ - 8x² - 7