Question

Given two functions j(x)=−6x+2 and k(x)=2+4x , what is the function rule for (kj)(x) ? (kj)(x)=−24x2+4x+4 (kj)(x)=24x2−4x+4 (kj)(x)=24x2−4x−4 (kj)(x)=−24x2−4x+4

Answer 1

Value of function
`\left (kj\right)\left(x\right)` is
`-24x^2-4x+4`

Explanation:

The function
`\left (kj\right)\left(x\right)` can be written as,

`\left (kj\right)\left(x\right)=k\left(x\right)* j\left(x\right)`

Now,
`k\left(x\right)=2+4x` and
`j\left(x\right)=-6x+2`

Substituting the value,

`\left (kj\right)\left(x\right)=\left(2+4x\right)* \left(-6x+2\right)`

Applying FOIL method,

`2\left(-6x+2\right)+4x\left(-6x+2\right)`

Now apply distributive property,

`2\left(-6x\right)+2\left(2\right)+4x\left(-6x\right)+4x\left(2\right)`

Simplifying,

Since product of negative number and positive number is always negative number.

`-12x+4-24x^(2)+8x`

Combining like terms,

`4-24x^(2)+8x-12x`

`4-24x^(2)-4x`

Rearranging,

`-24x^(2)-4x+4`

Hence the value of the function according to given rule is
`-24x^(2)-4x+4`.