Perform the indicated operation - Show Work Please!

Question

f(t) = -t - 4

g(t) = t^3 - 3

Find f(g(t^2))

 

Final Answer is meant to be -t^6 - 1

Answer 1

Since g(t) = t³ - 3, we have g(t²) = (t²)³ - 3 = t⁶ - 3.

 

Since f(t) = -t - 4, we have f(g(t²)) = f(t⁶ - 3) = -(t⁶ - 3) - 4 = -t⁶ - 1.