SOLUTION: Given that 𝑓(𝑡) = −𝑡^2 − 5𝑡 and 𝑔(𝑡) = 2𝑡 − 1, a) Find the expression of (𝑔𝑜𝑓)(𝑡) b) Compute (𝑓𝑜𝑔) (1/2).

Algebra ->  Functions -> SOLUTION: Given that 𝑓(𝑡) = −𝑡^2 − 5𝑡 and 𝑔(𝑡) = 2𝑡 − 1, a) Find the expression of (𝑔𝑜𝑓)(𝑡) b) Compute (𝑓𝑜𝑔) (1/2).      Log On


   

Question 1135931: Given that 𝑓(𝑡) = −𝑡^2 − 5𝑡 and 𝑔(𝑡) = 2𝑡 − 1,
a) Find the expression of (𝑔𝑜𝑓)(𝑡)
b) Compute (𝑓𝑜𝑔) (1/2).
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
Given:
f%28t%29+=-t%5E2+-5t+
+g%28t%29+=+2t+-+1
a) Find the expression of (𝑔𝑜𝑓)(𝑡)
(𝑔𝑜𝑓)(𝑡)=g%28f%28t%29%29
(𝑔𝑜𝑓)(𝑡)=g%28-t%5E2+-5t%29
(𝑔𝑜𝑓)(𝑡)=2%28-t%5E2+-5t%29-1
(𝑔𝑜𝑓)(𝑡)=-2t%5E2+-10t-1

b) Compute (𝑓𝑜𝑔) (1%2F2).
first find
(𝑓𝑜𝑔) (x)=f%28g%28x%29%29
(𝑓𝑜𝑔) (x)=f%28+2t+-+1%29
(𝑓𝑜𝑔) (x)=-%28+2t+-+1%29%5E2-5%282t+-+1%29
(𝑓𝑜𝑔) (x)=-%284+t%5E2+-+4+t+%2B+1%29-%2810t+-+5%29
(𝑓𝑜𝑔) (x)=-4+t%5E2+%2B4+t+-+1-10t+%2B+5
(𝑓𝑜𝑔) (x)=-4+t%5E2++-6t+%2B+4
now find
(𝑓𝑜𝑔) (1%2F2)=-4+%281%2F2%29%5E2++-6%281%2F2%29+%2B+4
(𝑓𝑜𝑔) (1%2F2)=-4+%281%2F4%29++-3+%2B+4
(𝑓𝑜𝑔) (1%2F2)=-1++-3+%2B+4
(𝑓𝑜𝑔) (1%2F2)=-4+%2B+4
(𝑓𝑜𝑔) (1%2F2)=0