Given that𝑓(𝑥)=2𝑥−3 and 𝑔(𝑥)=1−𝑥4solve (𝑓∘𝑔−1)(𝑥)=(𝑓∘𝑔)(𝑥).

To solve the equation (𝑓∘𝑔−1)(𝑥)=(𝑓∘𝑔)(𝑥), we first need to understand what the notation means.

The notation (𝑓∘𝑔)(𝑥) means f(g(x)), i.e., the function f is applied to the result of function g(x). Similarly, (𝑓∘𝑔−1)(𝑥) means f(g^(-1)(x)), i.e., the function f is applied to the inverse of function g(x).

Given 𝑓(𝑥)=2𝑥−3 and 𝑔(𝑥)=1−𝑥^4, we can write:

(𝑓∘𝑔)(𝑥) = f(g(x)) = 2(1-x^4) - 3 = 2 - 2x^4 - 3 = -2x^4 - 1.

To find (𝑓∘𝑔−1)(𝑥), we first need to find the inverse of g(x), g^(-1)(x).

The function 𝑔(𝑥)=1−𝑥^4 can be rewritten as x = sqrt[4]{1 - g}, so g^(-1)(x) = sqrt[4]{1 - x}.

Then, (𝑓∘𝑔−1)(𝑥) = f(g^(-1)(x)) = 2sqrt[4]{1 - x} - 3.

Setting (𝑓∘𝑔−1)(𝑥) = (𝑓∘𝑔)(𝑥), we get:

-2x^4 - 1 = 2sqrt[4]{1 - x} - 3.

Solving this equation will give us the value(s) of x that satisfy the equation. However, this is a complex equation that may not have a simple algebraic solution. It may require numerical methods to solve.