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Show that (fof-1) (x)=x and (F-1 of)(x) = x for the following pair of functions.f(x) = 5-4x, f'(x) =5-754Show that (fof-1)(x) = x.(fof- ')(x) = 0Write the expression for the composition.= x(Do not simplify. Type an exact answer, using radicals as needed.)

Show that fof1 xx and F1 ofx x for the following pair of functionsfx 54x fx 5754Show that fof1x xfof x 0Write the expression for the composition xDo not simplif class=

Respuesta :

To obtain the expression for the composition of the function of the inverse function of x, the following steps are necessary:

Step 1: Write out the expression for the function of x and the inverse function of x, as below:

[tex]\begin{gathered} f(x)=\sqrt[5]{5-4x} \\ ^{}f^{-1}(x)=\frac{5-x^5}{4} \end{gathered}[/tex]

Step 2: Write out the expression for the composition of the function of the inverse function of x, as below:

[tex](f^{-1}Of))(x)=^{}\frac{5-(\sqrt[5]{5-4x})^5}{4}[/tex]

Thus, the above is how the expression for the composition of the function of the inverse function of x is to be written out

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