SOLUTION: Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if a(x) = 2x - 5 and b(x) = 4 + 7x

SOLUTION: Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if a(x) = 2x - 5 and b(x) = 4 + 7x - 3x^2.

Question 1209326: Let a(x) and b(x) be functions. Find (a\circ b)(3) - (b\circ a)(3) if a(x) = 2x - 5 and b(x) = 4 + 7x - 3x^2.
Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.
Let a(x) and b(x) be functions. Find (a o b)(3) - (b o a)(3)
if a(x) = 2x - 5 and b(x) = 4 + 7x - 3x^2.
~~~~~~~~~~~~~~~~~~~~~~~

        They do not ask to express implicitly the composite functions.

        Therefore, the shortest and the easiest way is to calculate the interior argument
        of the composite function, then calculate the values of the composite functions
        and then take their difference.

For (a o b)(3) = a(b(3)), we calculate first b(3) = 4 + 7*3 - 3*3^2 = -2.

Then we calculate  a(b(3)) = a(-2) = 2*(-2) - 5 = -9.



For (b o a)(3) = b(a(3)), we calculate first a(3) = 2*3 - 5 = 1.

Then we calculate  b(a(3)) = b(1) = 4 + 7*1 - 3*1^2 = 8.



Finally,  (a o b)(3) - (b o a)(3) = -9 - 8 = -17.    ANSWER

Solved.

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