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 [tex] f\circ g(x) [/tex] is defined as [tex] f(g(x)) [/tex].
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 [tex] f(x)=3x^3, g(x)=x-1 [/tex]
[tex] f\circ g(x)=f[g(x)] [/tex]
Now plug in [tex] g(x)=x-1 [/tex], we get
[tex] f\circ g(x)=f[g(x)]=f(x-1) [/tex]
It is given that [tex] f(x)=x^3 [/tex], using this we need to find [tex] f(x-1). [/tex]
Replace x by x-1 in f(x),
[tex] f[g(x)]=f(x-1)=3(x-1)^3 [/tex]
Now we need to find [tex] f(g(3)) [/tex],
[tex] f[g(3)]=3(3-1)^3=3(2^3)=3*8=24 [/tex]
So [tex] f(g(3)=24 [/tex]
So the soiution is (B): 24
Solution for question (43):
[tex] h(x)=6x^2+5x-13 [/tex]
Plug in [tex] x=-5, [/tex] to find h(-5):
[tex] h(-5)=6*(-5)^2+5*(-5)-13 [/tex]
[tex] =6*25+5*-5-13\\ =112 [/tex]+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
[tex] h(t)=-16t^2+64t [/tex]
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),
[tex] h(2)=-16*2^2+64*2 [/tex]
[tex] =-16*4+128=-64+128
[/tex]
[tex] =64 [/tex]
Thus the answer for (44) is (A): 64.
