Option D:
is the value of ![(c \circ d)(x)](/tpl/images/0552/4026/71853.png)
Explanation:
Given that the two functions
and ![d(x)=x^{2} +5x](/tpl/images/0552/4026/e9051.png)
To find the value of
:
The value of
can be determined using the formula,
![(c \circ d)(x)=c[d(x)]](/tpl/images/0552/4026/3feb5.png)
First, we shall substitute
in the above formula.
Thus, we have,
![(c \circ d)(x)=c[x^2+5x]](/tpl/images/0552/4026/5fb21.png)
Now, substituting
in the function
, we get,
![(c \circ d)(x)=4(x^2+5x)-2](/tpl/images/0552/4026/3d340.png)
Simplifying the terms, we get,
![(c \circ d)(x)=4x^2+20x-2](/tpl/images/0552/4026/ed248.png)
Therefore, the value of
is ![4x^{2} +20x-2](/tpl/images/0552/4026/4c1b2.png)
Hence, Option D is the correct answer.