Question

Let f , g and h be functions from R to R . Show that

Answer 1

The given functions are f:R→R, g:R→R and h:R→R.

On solving left hand side, we get

( ( f+g )οh )( x )=( f+g )( h( x ) ) =f( h( x ) )+g( h( x ) ) =( foh )( x )+( goh )( x ) ={ ( foh )+( goh ) }( x )

It is equal to right hand side.

Hence, ( f+g )oh=foh+goh.

On solving left hand side, we get

( ( f⋅g )oh )( x )=( f⋅g )( h( x ) ) =f( h( x ) )⋅g( h( x ) ) =( foh )( x )⋅( goh )( x ) ={ ( foh )⋅( goh ) }( x )

It is equal to right hand side.

Hence, ( f⋅g )oh=( foh )⋅( goh ).