Question

Let f(x) = x raise to power 2 + 4x - 12 and g

Answer 1

As given by the question

There are given that the function:

`\begin{gathered} f(x)=x^2+4x-12 \\ g(x)=-12x^2-2x-10 \end{gathered}`

Now,

(a): (f + g)(-5)

Then,

`(f+g)(-5)=(f(-5)+g(-5))`

So,

`\begin{gathered} (f+g)(-5)=(f(-5)+g(-5)) \\ =((-5)^2+4(-5)-12)+(-12(-5)^2-2(-5)-10) \\ =(25-20-12)+(-300+10-10) \\ =-7-300 \\ =-307 \end{gathered}`

Hence, the value of the given addition is -307.

Now,

(b) ( f - g)(-5)

Then,

`(f-g)(-5)=(f(-5)-g(-5))`

So,

`\begin{gathered} (f-g)(-5)=(f(-5)-g(-5)) \\ =((-5)^2+4(-5)-12)-(-12(-5)^2-2(-5)-10) \\ =(25-20-12)-(-300+10-10) \\ =-7+300 \\ =293 \end{gathered}`

Hence, the value of the given subtraction is 293.