Question

Let k ( x ) = 2 x + 3 and m ( x ) = 3 x 2 + 7 x − 10 . Find the indicated value. M ( k ( − 4 ) ) =

Answer 1

Answer: $30$

Step-by-step explanation:

Given

$k(x)=2x+3$

$M(x)=3x^2+7x-10$

$M\left(k(x)\right)$ is given by replacing the $x$ by $k(x)$ from the $M(x)$

$\Rightarrow M\left(k(x)\right)=3(2x+3)^2+7(2x+3)-10\\\Rightarrow M\left(k(x)\right)=3(4x^2+9+12x)+14x+21-10\\\Rightarrow M\left(k(x)\right)=12x^2+50x+38$

Now, $M\left(k(-4)\right)$ is

$\Rightarrow M\left(k(-4)\right)=12(-4)^2+50(-4)+38\\\Rightarrow M\left(k(-4)\right)=192-200+38\\\Rightarrow M\left(k(-4)\right)=30$