The inverse of the function y = (x+7)² is [tex]f^{-1}x=\sqrt{x} - 7[/tex]
From the given function f(x) = (x+7)²
Let y = f(x), the expression becomes:
y = (x+7)²
Replace y with x
x = (y+7)²
Maker y the subject of the formula
x = (y+7)²
Take the square root of both sides
√x = √(y+7)²
√x = y + 7
y = √x - 7
Replace y with [tex]f^{-1}x[/tex]
[tex]f^{-1}x=\sqrt{x} - 7[/tex]
Hence the inverse of the function y = (x+7)² is [tex]f^{-1}x=\sqrt{x} - 7[/tex]
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