Consider the function
f(x) = 8x^3 +1.

If f(g(x)) = x and g(f(x)) = x , find g(x) ?

If f(g(x)) = x and g(f(x)) = x , than   and this can be calculated by finding the inverse of the given function f(x).

Given :

Given that f(g(x)) = x it means that:

It is also given that g(f(x)) = x that means:

Now, the inverse of f(x) is given by the following calculation:

Now, replace f(x) with y in the above equation.

Now, replace y with x and x with y and evaluate 'y'.

Now, replace y with in the above equation.

For more information, refer to the link given below:

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And

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So :

And

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So to find g(x) , we must find the inverse of f(x) .

Let's do it .....

Subtract the sides of the equation minus 1

Divided the sides of the equation by 8

From the sides of the equation, we take the radical with interval 3

So ;

Now we find g(x) which is :

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And we're done.

Thanks for watching buddy good luck.

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