The inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
How to determine the inverse function?
The function is given as:
f(x) = (x + 3)^3 - 1
Rewrite as:
y = (x + 3)^3 - 1
Swap x and y
x = (y + 3)^3 - 1
Add 1 to both sides
(y + 3)^3 = x + 1
Take the cube root of both sides
[tex]y + 3 = \sqrt[3]{x + 1}[/tex]
Subtract 3 from both sides
[tex]y = \sqrt[3]{x + 1} - 3[/tex]
Rewrite as:
[tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
Hence, the inverse function of f(x) is [tex]f^{-1}(x) = \sqrt[3]{x + 1} - 3[/tex]
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