Lee S.

asked • 08/24/16

Perform the indicated operation - Show Work

g(t) = -3t^2 + 4
f(t) = 2t - 3
Find g(f(t^2))

1 Expert Answer

By:

Neal D. answered • 08/24/16

Tutor
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Education Made Understandable

Jennifer D.

tutor
Neal has the correct answers to the intermediate steps in the solution, but there are a few details missing about the operations needed to perform them.
 
To help clarify, here is what you need to do in a procedural format:
  1. As shown above, f(t) is nested into g(t), therefore you need to solve f(t2) first. Hence that's why you have 2t2-3= f(t2).
  2. When you substitute the result of Step 1 back into the nested g(t) function, you get:
                   g(f(t2)) = g(2t2-3) = -3(2t2-3)2+4. The (2t2-3)2 term needs expanded before we obtain the final answer.
   
    3. Expand (2t2-3)= (2t2-3)(2t2-3) = 4t4-6t2-6t2+9 = 4t4-12t2+9
 
    4. Substitute result of Step 3 back into nested g(t) function and solve for final answer:
                    -3(4t4-12t2+9)+4 = -12t4+36t2-27+4 = -12t4+36t2-23. You're Done!
 
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08/25/16

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