Answered

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given f(x) = x² + 4x -5find f(x) inverse

Sagot :

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]

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