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((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((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((a)/(b)\right)(x)=(a(x))/(b(x))`

`\left((a)/(b)\right)(x)=(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((a)/(b)\right)(x)=(4x+9)/(3x-5)`.