Question

If c(x) = 4x – 2 and d(x) = x2 + 5x, what is (cºo)(x)?
4x2 + 18x2 – 10x
O x² + 9x-2
16x2 + 4x - 6
O 4x2 + 20x-2

Answer 1

Option D: $4x^{2} +20x-2$ is the value of $(c \circ d)(x)$

Explanation:

Given that the two functions $c(x)=4 x-2$ and $d(x)=x^{2} +5x$

To find the value of $(c \circ d)(x)$:

The value of $(c \circ d)(x)$ can be determined using the formula,

$(c \circ d)(x)=c[d(x)]$

First, we shall substitute $d(x)=x^{2} +5x$ in the above formula.

Thus, we have,

$(c \circ d)(x)=c[x^2+5x]$

Now, substituting $x=x^2+5x$ in the function $c(x)=4 x-2$, we get,

$(c \circ d)(x)=4(x^2+5x)-2$

Simplifying the terms, we get,

$(c \circ d)(x)=4x^2+20x-2$

Therefore, the value of $(c \circ d)(x)$ is $4x^{2} +20x-2$

Hence, Option D is the correct answer.