213,368 views
1 vote
1 vote
The functionx > or equal to 8f(x) = -9/x – 8+5has an inverse f-1(x) defined on the domain x < or equal to 5. Find the inverse.

The functionx > or equal to 8f(x) = -9/x – 8+5has an inverse f-1(x) defined on-example-1
User Zacky Pickholz
by
2.7k points

1 Answer

14 votes
14 votes

Here we have the function:


f(x)=-9\sqrt[]{x-8}+5;x>8

We're going to find the inverse function;


f^(-1)(x)

For this, we're going to solve the following equation for x: (Let f(x) be y).


y=-9\sqrt[]{x-8}+5

We could square both sides as follows:


\begin{gathered} y-5=-9\sqrt[]{x-8} \\ (y-5)^2=(-9\sqrt[]{x-8)}^2) \end{gathered}

Now, we could rewrite:


\begin{gathered} y^2-10y+25=81(x-8) \\ y^2-10y+25=81x-648 \end{gathered}

And then solve for x:


\begin{gathered} y^2-10y+25=81x-648 \\ y^2-10y+25+648=81x \\ y^2-10y+673=81x \\ (y^2-10y+673)/(81)=x \end{gathered}

Finally, we can write:


f^(-1)(x)=(x^2-10x+673)/(81)

User Bux
by
2.1k points