Question

Let f(t)=(t^{2}+7 t+8)(2 t^{2}+2) f(t)=8 t^{3}+42 t^{2}+36 t+14 Find f(4) =

Answer 1

To calculate f(4) for the given function, replace t with 4 and perform the arithmetic operations to obtain f(4) = 1342.

Step-by-step explanation:

To find f(4) when f(t) = 8t3 + 42t2 + 36t + 14, we substitute t with 4 and calculate the result:

f(4) = 8(4)3 + 42(4)2 + 36(4) + 14

Now, perform the operations step by step:

1. Calculate the cube of 4: 43 = 64.
2. Multiply this result by 8: 8 × 64 = 512.
3. Find the square of 4: 42 = 16.
4. Multiply this by 42: 42 × 16 = 672.
5. Perform the multiplication of 36 by 4: 36 × 4 = 144.
6. Add all these values together with 14 to find f(4).
7. So, f(4) = 512 + 672 + 144 + 14 = 1342.

Hence, f(4) = 1342.