Question

Need help on this math problem!!!

Answer 1

Answer:

$(fof^{-1})(x)=x$

Step-by-step explanation:

Composition of two functions f(x) and g(x) is represented by,

(fog)(x) = f[g(x)]

If a function is,

f(x) = (-6x - 8)² [where x ≤ $-\frac{8}{6}$]

Another function is the inverse of f(x),

$f^{-1}(x)=-\frac{\sqrt{x}+8}{6}$

Now composite function of these functions will be,

$(fof^{-1})(x)=f[f^{-1}(x)]$

                  = $[-6(\frac{\sqrt{x}+8}{6})-8]^{2}$

                  = $[-\sqrt{x}+8-8]^2$

                  = $(-\sqrt{x})^2$

                  = x

Therefore, $(fof^{-1})(x)=x$