Question

Please help. 24 points!!

Answer 1

The given function is,

$f(x)= \frac{2x-1}{x+5}$.

Or, $y= \frac{2x-1}{x+5}$

To find the inverse of a function, first step is to switch x and y. Therefore,

$x= \frac{2y-1}{y+5}$

Next stpe is to solve the above equation for y t get the inverse f f(x). Hence, multiply each sides by y + 5 to get rid of fraction form. So,

$x*(y+5)= \frac{2y-1}{y+5}*(y+5)$

xy + 5x = 2y - 1

xy = 2y - 1 - 5x Subtract 5x from each sides to isolate y.

xy - 2y = -5x - 1 Subtract 2y from each sides.

y(x - 2) = -5x -1 Take out the common factor y.

$\frac{y(x-2)}{(x-2)} =\frac{(-5x-1)}{(x-2)}$ Divide each sides by x-2.

$y=\frac{(-5x-1)}{(x-2)}$

So, $f^-1(x)=\frac{-5x-1}{x-2}$

Now when we will compare $f^-1(x)=\frac{-5x-1}{x-2}$ with $f^-1(x)=\frac{ax+b}{cx+d}$ then we will get a = -5, b = -1, c = 1 and d=-2

So, $\frac{a}{c} =\frac{-5}{1} =-5$

Hope this helps you!