Question

Given

f
(
x
)
=
−
x
−
2
f(x)=−x−2, find
f
(
−
6
)
f(−6).

Answer 1

`\boxed{\tt \: f( - 6) = 4}`

Explanation:

Given polynomial :-

`\sf \: f(x) = - x - 2`

To Find :-

`\sf \: f( - 6)`

Solution :-

`\sf \implies \: f(x) = - x - 2`

`\underline{ \rm \: Substitute \: the \: value \: of \: x \: that \: is \: 6 \: i nstead \: of \: x \: on \: the \: LHS \: and \: RHS \: of \: the \: given \: equation :-}`

That is ,

`\sf \implies \: f( - 6) = - ( - 6) - 2`

`\underline{ \rm \: Simplify \: the \: RHS \: on \: t he \: given \: equation :-}`

As we know that "-" and "-" equals to "+". So "-(-6)" would be represented as +6 (6).

`\sf \implies \: f( - 6) = + 6 - 2`

Subtract 6 and 2 :-

`\sf \implies \: f( - 6) = 6 - 2`

`\sf \implies \: f( - 6) = 4`

This can't be simplified more . Hence ,

`\rm \: The \: value \: of \: f(-6) \: would \: be \: \boxed{ \bf 4} \rm .`

`\rule{175pt}{2pt}`

I hope this helps!