Answer for question (42):
We need to find the composition of two functions f(x) and g(x).
By the definition, the composition of two functions
is defined as
.
That is, The composition of two functions f and g is the new function , by performing g first and then performing f.
Here we have
![f(x)=3x^3, g(x)=x-1](https://img.qammunity.org/2019/formulas/mathematics/middle-school/pjbqle86dtugdq6udp6w836mupn4u9gi9v.png)
![f\circ g(x)=f[g(x)]](https://img.qammunity.org/2019/formulas/mathematics/middle-school/zlexnfmdciwylhvyorfe3zhgq89392eh49.png)
Now plug in
, we get
![f\circ g(x)=f[g(x)]=f(x-1)](https://img.qammunity.org/2019/formulas/mathematics/middle-school/xarsby2r5x4iqnvjc5ep02s9q90xspriei.png)
It is given that
, using this we need to find
Replace x by x-1 in f(x),
![f[g(x)]=f(x-1)=3(x-1)^3](https://img.qammunity.org/2019/formulas/mathematics/middle-school/c4asx0390k93p0j3j1ymzlawt97p7clw14.png)
Now we need to find
,
![f[g(3)]=3(3-1)^3=3(2^3)=3*8=24](https://img.qammunity.org/2019/formulas/mathematics/middle-school/9bjhrmih7bivlbcwmpj5bhjg61058enk07.png)
So
![f(g(3)=24](https://img.qammunity.org/2019/formulas/mathematics/middle-school/x4vordb0bo0h6791kfj39j3kuyv5y5a61o.png)
So the soiution is (B): 24
Solution for question (43):
![h(x)=6x^2+5x-13](https://img.qammunity.org/2019/formulas/mathematics/middle-school/thjo3ypzrf814zm0vnqciy9z8qs5fcuzf3.png)
Plug in
to find h(-5):
![h(-5)=6*(-5)^2+5*(-5)-13](https://img.qammunity.org/2019/formulas/mathematics/middle-school/zjks109egr6gc666qjbis27avrp4fzu2xt.png)
+5(-5)-13 [/tex]
Thus the answer for (43) is (D): 112.
Solution for question (44):
The height of a ball projected into the air can be represented by the function is
![h(t)=-16t^2+64t](https://img.qammunity.org/2019/formulas/mathematics/middle-school/k1bp3m37wqbrjfkv1l40r4pfs8dbozbovs.png)
Then to find the height of the ball in feet when it has been in the air for 2 seconds:
Plug in t=2 in h(t),
![h(2)=-16*2^2+64*2](https://img.qammunity.org/2019/formulas/mathematics/middle-school/w3wxb24zvbs9izixpme5yel0d6ywgay4ou.png)
![image](https://img.qammunity.org/2019/formulas/mathematics/middle-school/feh3xd6dwf0j6w1ih7b8pro4dxag9jhoij.png)
![=64](https://img.qammunity.org/2019/formulas/mathematics/middle-school/1zrukh7822inc7a664ax24jip2v9q1e6r4.png)
Thus the answer for (44) is (A): 64.