Suppose a(x) = 3x - 7 and b(x) = 2 - x^3. Find a(b(3)) - b(a(3)).
Thank you for helping me!
To find a(b(3)), we first need to find the value of b(3) by substituting 3 for x in the expression for b(x).
b(x) = 2 - x^3
b(3) = 2 - (3)^3
= 2 - 27
= -25
Now that we know b(3) is equal to -25, we can find a(b(3)) by substituting -25 into the expression for a(x).
a(x) = 3x - 7
a(b(3)) = 3(-25) - 7
= -75 - 7
= -82
Next, to find b(a(3)), we need to find the value of a(3) by substituting 3 for x in the expression for a(x).
a(x) = 3x - 7
a(3) = 3(3) - 7
= 9 - 7
= 2
Now, substitute 2 into the expression for b(x) to find b(a(3)).
b(x) = 2 - x^3
b(a(3)) = 2 - (2)^3
= 2 - 8
= -6
Finally, find a(b(3)) - b(a(3)).
a(b(3)) - b(a(3)) = -82 - (-6)
= -82 + 6
= -76
Therefore, a(b(3)) - b(a(3)) is equal to -76.