Question

Can anyone help me with these three plz ??? I have no clue how to do this

Answer 1

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
`f\circ g(x)` is defined as
`f(g(x))`.

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`

`f\circ g(x)=f[g(x)]`

Now plug in
`g(x)=x-1`, we get

`f\circ g(x)=f[g(x)]=f(x-1)`

It is given that
`f(x)=x^3`, using this we need to find
`f(x-1).`

Replace x by x-1 in f(x),

`f[g(x)]=f(x-1)=3(x-1)^3`

Now we need to find
`f(g(3))`,

`f[g(3)]=3(3-1)^3=3(2^3)=3*8=24`

So
`f(g(3)=24`

So the soiution is (B): 24

Solution for question (43):

`h(x)=6x^2+5x-13`

Plug in
`x=-5,` to find h(-5):

`h(-5)=6*(-5)^2+5*(-5)-13`

`=6*25+5*-5-13\\ =112`+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`

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`

`image`

`=64`

Thus the answer for (44) is (A): 64.