Question

F(x) if f(x-2)=2-x

RSM IS KILLING ME HERE
also there's some more like this but if ik how to do this i might be able to figure those out

thanks!

Answer 1

Let's spot out.

• f(x-2)=2-x

Put x+2 in place of x

• f(x+2-2)=2-(x+2)
• f(x)=2-x-2
• f(x)=-x

Answer 2

`f(x)=-x`

Explanation:

`f(x-2)=2-x`

To change
`f(x - 2)` into
`f(x)`, substitute
`x=x+2`:

`\implies f((x+2)-2)=f(x+2-2)=f(x)`

Therefore, substitute
`x=x+2` into both sides of
`f(x-2)=2-x`:

`\implies f((x+2)-2)=2-(x+2)`

`\implies f(x)=-x`