The function g(x) is [tex]g(x) = (x + 7)^3[/tex]
How to determine the function g(x)?
The function f(x) is given as:
[tex]f(x) = \sqrt[3]{x} - 7[/tex]
If f(g(x)) = g(f(x)) = x, then the functions are inverse functions.
So, we have:
[tex]f(x) = \sqrt[3]{x} - 7[/tex]
Rewrite as:
[tex]y = \sqrt[3]{x} - 7[/tex]
Swap x and y
[tex]x = \sqrt[3]{y} - 7[/tex]
Add 7 to both sides
[tex]x + 7 = \sqrt[3]{y}[/tex]
Take the cube of both sides
[tex]y = (x + 7)^3[/tex]
This implies that
[tex]g(x) = (x + 7)^3[/tex]
Hence, the function g(x) is [tex]g(x) = (x + 7)^3[/tex]
Read more about inverse functions at:
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