Question 1153070


Inverse function of

{{{p(x) = - (sqrt (-x+2)) -3}}}

replace {{{p(x) }}} with {{{y}}}

{{{y = - (sqrt (-x+2)) -3}}}.....swap variables

{{{x= - (sqrt (-y+2)) -3}}}.......solve for {{{y}}}

{{{x+3= - (sqrt (-y+2)) }}}......both sides divide by {{{-1}}}

{{{-x-3=  sqrt (-y+2) }}}.....squre both sides

{{{(-x-3)^2=  -y+2 }}}

{{{y=  -(-x-3)^2+2 }}}

{{{y=  -(x^2 + 6 x + 9)+2}}}

{{{y=  -x^2 - 6 x- 9+2}}}

{{{y=  -x^2 - 6 x- 7}}}

{{{p^-1(x) =y}}}

{{{p^-1(x) =-x^2 - 6 x- 7}}}-> inverse