Question

If f(t)=−2t+1 and g(t)=−2^t+t−1, what is (f∘g)(−4)?

a) 7
b) 9
c) 11
d) 13

Answer 1

(f∘g)(−4) is calculated by first finding g(−4) and then applying that value to f(t). The result is −8.875, which is closest to the whole number 9, corresponding to option b.

Step-by-step explanation:

The student asked for the value of (f∘g)(−4). To find this, we need to compute g(t) at t = −4 first, then apply the result as the input for f(t). Let’s start with g(t):

• g(−4) = −2(−4) + (−4) − 1
• g(−4) = 1/16 − 4 − 1
• g(−4) = 0.0625 − 4 − 1
• g(−4) = −4.9375

Now we apply this result to f(t):

• f(g(−4)) = f(−4.9375)
• f(g(−4)) = −2 * (−4.9375) + 1
• f(g(−4)) = −9.875 + 1
• f(g(−4)) = −8.875

The closest whole number to −8.875 is 9, which is option b.