Answered

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Find the inverse function of f.f(x) = 7 - 9x3f^-1(x) =

Find The Inverse Function Of Ffx 7 9x3f1x class=

Sagot :

ANSWER

[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]

EXPLANATION

We want to find the inverse function of the given function:

[tex]f(x)=7-9x^3[/tex]

To do this, we have to make x the subject of the formula.

Let f(x) be y:

[tex]\begin{gathered} y=7-9x^3 \\ 9x^3=7-y \\ x^3=\frac{7-y}{9} \\ \Rightarrow x=\sqrt[3]{\frac{7-y}{9}} \end{gathered}[/tex]

Now, replace x with f^(-1)(x) and y with x:

[tex]f^{-1}(x)=\sqrt[3]{\frac{7-x}{9}}[/tex]

That is the inverse function of f.

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