Question

What is equal to `(f-g)(-5)? color(white)("d")` `color(white)("d")` `f(x)=2+x", "color(white)("d")g(x)=x^2+5`

Answer 1

`-33`

Explanation:

`color(blue)("Preamble")`

Note that `f and g` are just names. The question poser has assigned those names to the equation structures given.

So within the context OF THIS QUESTION whenever you see the name `g` you know they are talking about `x^2+5`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Answering the question")`

Set `y_1=f( color(red)(x))=2+color(red)(x)`

So by substituting (-5) for `x` we have:

`y_1=f( color(red)(-5))=2+(color(red)(-5)) =-3`
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Set `y_2=g(color(red)(x))=color(red)(x)^2+5`

So by substituting (-5) for `x` we have:

Set `y_2=g(color(red)(-5))=(color(red)(-5))^2+5 = +30`

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

`(f-g)(-5)color(white)("d")=color(white)("d")y_1-y_2color(white)("ddd")=color(white)("ddd")-3-30color(white)("d")=color(white)("d")-33`