Use the functions f(x)=(1/8)x-3 and g(x)=x^3 to find the indicated value or function `f^-1(g^-1(1))`  

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The function `f(x) = x/8 - 3` and `g(x) = x^3` .

For a function f(x), `f^-1(x)` is related to f(x) by `f(f^-1(x)) = x`

Here, `f(x) = x/8 -3`

=> `(f^-1(x))/8 - 3 = x`

=> `f^-1(x) = (x + 3)*8`

Similarly, `g^-1(x) = root(3) x`

`f^-1(g^-1(x)) = f^-1(root(3) x) = (root(3) x + 3)*8`

`f^-1(g^-1(1)) = (root(3) 1 + 3)*8 = 4*8 = 32`

The value of `f^-1(g^-1(1)) = 32`

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