Given:
[tex]f(x)=-x[/tex]
Required:
[tex]We\text{ need to find }f^{-1}(x).[/tex]
Explanation:
[tex]\text{ Let f\lparen x\rparen=y and }x=f^{-1}(y).[/tex][tex]Substitute\text{ f\lparen x\rparen=y and }x=f^{-1}(y)\text{ in the equation f\lparen x\rparen=-x.}[/tex][tex]y=-f^{-1}(y).[/tex]
Multiply both sides of the equation by (-1).
[tex](-1)y=-(-1)f^{-1}(y).[/tex][tex]-y=f^{-1}(y).[/tex][tex]f^{-1}(y)=-y[/tex]
Replace y=x in the equation.
[tex]f^{-1}(x)=-x[/tex]
Final answer:
[tex]f^{-1}(x)=-x[/tex]
