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- Which is the inverse or the funcion f(x)=x²-16?​

Sagot :

Given:

The function is:

[tex]f(x)=x^2-16[/tex]

To find:

The inverse of the function.

Solution:

We have,

[tex]f(x)=x^2-16[/tex]

Step 1: Substitute [tex]f(x)=y[/tex].

[tex]y=x^2-16[/tex]

Step 2: Interchange x and y.

[tex]x=y^2-16[/tex]

Step 3: Isolate y.

[tex]x+16=y^2[/tex]

[tex]\pm \sqrt{x+16}=y[/tex]

[tex]y=\pm \sqrt{x+16}[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex].

[tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex]

Therefore, the inverse function of the given function is [tex]f^{-1}(x)=\pm \sqrt{x+16}[/tex].

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