1. Let f(a,b) = 2a - 3b^2 + 7. If f(b,3) = 90, then what is b?
2. Suppose a(x) = 3x - 7 and b(x) = 2 - x^3. Find a(b(3)) - b(a(3)).
I sense more AOPS
1)
f(b,3) = 2b - 3(3)^2 + 7 = 2b - 20
2b - 20 = 90
2b = 110
b = 55
2)
b(3) = 2 - 3^3 = -25
a(3) = 3(3) - 7 = 2
a(b(3)) - b(a(3))
= a(-25) - b(2)
= 3(-25) - 7 - (2 - 2^3)
= -75 - 7 + 6
= -76
