Question

How do you solve this difficult algebra problem?

F(x)= 2x^2-5x+3 and G(x)=1-4x-x^2

Calculate f(-2) + g(2)

Answer 1

`10`

Explanation:

`"substitute "x=-2" into" f(x) " and "x=2" into "g(x)`

`f(-2)=2(-2)^2-5(-2)+3`

`color(white)(f-(2))=(2xx4)+(-5xx-2)+3`

`color(white)(f(-2))=8+10+3=21`

`g(2)=1-(4xx2)-(2)^2`

`color(white)(g(2))=1-8-4=-11`

`f(-2)+g(2)=21+(-11)=21-11=10`

Answer 2

`10`

Explanation:

The key realization is that `f(-2)` means that we will evaluate the function `f` at `x=-2`, and `g(2)` means we evaluate `g` at `x=2`.

Plugging in `-2` for `f`, we get

`f(-2)=2(-2)^2-5(-2)+3=21`

Plugging in `2` for `g`, we get

`g(2)=1-4(2)-(2)^2=1-8-4=-11`

We have been asked to find

`f(-2)+g(2)`, and since we have both values, we can sum them to get

`21-11=10`

Hope this helps!