The function is given as
[tex]f(x)=x^2+4x-5[/tex]To find the inverse of the function ,
[tex]y=x^2+4x-5[/tex]Replace x with y.
[tex]x=y^2+4y-5[/tex]Now solve for y,
Add 4 and subtract 4 in the RHS.
[tex]x=y^2+4y-5+4-4[/tex][tex]x=y^2+4y-9+4[/tex][tex]x=(y+2)^2-9[/tex][tex]x+9=(y+2)^2[/tex][tex](y+2)^2=x+9[/tex][tex]y+2=\pm\sqrt[]{x+9}[/tex][tex]y=\sqrt[]{x+9}-2[/tex][tex]y=-\sqrt[]{x+9}-2[/tex]Hence the inverse of the function is
[tex]y=\sqrt[]{x+9}-2,-\sqrt[]{x+9}-2[/tex]