Question

Given that 7B5x-3%7D" id="TexFormula1" title="f(x)=\frac{3x+4}{5x-7} \\ g(x)=\frac{7x+4}{5x-3}" alt="f(x)=\frac{3x+4}{5x-7} \\ g(x)=\frac{7x+4}{5x-3}" align="absmiddle" class="latex-formula"> . Determine ($g^{-1}$°$f^{-1}$)and the domain of their product.

Answer 1

Greetings from Brasil...

Solving the inverses of these functions and applying the composite we obtain:

(G⁻¹ о F⁻¹) = X

Note that (F⁻¹ о G⁻¹) also results in X (see second annex)