Question

use these functions a(x) =4x +9 and b(x) =3x -5 to complete the function operations listed below

Answer 1

Consider that we need to find $(a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)$.

Given:

The functions are:

$a(x)=4x+9$

$b(x)=3x-5$

To find:

The function operations $(a+b)(x), (a-b)(x), (ab)(x),\left(\dfrac{a}{b}\right)(x)$.

Solution:

We have,

$a(x)=4x+9$

$b(x)=3x-5$

Now,

$(a+b)(x)=a(x)+b(x)$

$(a+b)(x)=4x+9+3x-5$

$(a+b)(x)=7x+4$

Similarly,

$(a-b)(x)=a(x)-b(x)$

$(a-b)(x)=4x+9-(3x-5)$

$(a-b)(x)=4x+9-3x+5$

$(a-b)(x)=x+14$

And,

$(ab)(x)=a(x)b(x)$

$(ab)(x)=(4x+9)(3x-5)$

$(ab)(x)=12x^2-20x+27x-45$

$(ab)(x)=12x^2+7x-45$

And,

$\left(\dfrac{a}{b}\right)(x)=\dfrac{a(x)}{b(x)}$

$\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}$

Therefore, the required functions are $(a+b)(x)=7x+4$, $(a-b)(x)=x+14$, $(ab)(x)=12x^2+7x-45$ and $\left(\dfrac{a}{b}\right)(x)=\dfrac{4x+9}{3x-5}$.