Let f(t)=2t²+3t-4
f(t+1)=f(t)+4t+5 TRUE or FALSE
answer is true, but i don't know how to get it, please help :(
re-arrange your answer to fit their answer.
I hope you had
f(t+1) = 2t² + 4t + 2 + 3t + 3 - 4 after you expanded
which is
f(t+1) = (2t² + 3t - 4) + 4t + 5
= f(t) + 4t + 5
To determine whether the statement "f(t+1) = f(t) + 4t + 5" is true or false, we can follow these steps:
1. Substitute t + 1 into the original function f(t):
f(t+1) = 2(t+1)² + 3(t+1) - 4
2. Expand and simplify the expression:
f(t+1) = 2(t² + 2t + 1) + 3t + 3 - 4
= 2t² + 4t + 2 + 3t + 3 - 4
= 2t² + 3t - 4 + 4t + 5
3. Compare the result with the expression f(t) + 4t + 5:
f(t+1) = f(t) + 4t + 5
By comparing the simplified expressions, we can see that they are identical:
f(t+1) = f(t) + 4t + 5
Therefore, the given statement "f(t+1) = f(t) + 4t + 5" is true.