How do you find the inverse of $h (X) = \frac{5}{2 x + 3}$ $h(X)= 5 / (2x + 3)$ and is it a function?

Question

3669 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-03-20T03:49:50

The inverse of a function can be found algebraically by switching the x and y values

$y = \frac{5}{2 x + 3}$ $y = 5/(2x + 3)$

$x = \frac{5}{2 y + 3}$ $x = 5/(2y + 3)$

$x (2 y + 3) = 5$ $x(2y + 3) = 5$

$2 y + 3 = \frac{5}{x}$ $2y + 3 = 5/x$

$2 y = \frac{5 - 3 x}{x}$ $2y = (5 - 3x)/x$

$y = \frac{5 - 3 x}{2 x}$ $y = (5 - 3x)/(2x)$

$h^{- 1} (x) = \frac{5 - 3 x}{2 x}$ $h^-1(x) = (5 - 3x)/(2x)$

Here are a few things to remember when finding the inverse of a function:

The y must be isolated (all alone on one side of the equation).
Don't forget the #h^-1(x) notation. I have been docked marks before from forgetting to include this element in my answer.
The inverse of a function can be found graphically by reflecting the original function over the line $y = x$ $y = x$

The first graph below is of the original function. The second is of the inverse.

graph{y = 5/(2x + 3) [-10, 10, -5, 5]}

graph{y = (5 - 3x)/(2x) [-4.933, 4.933, -2.466, 2.467]}

Practice exercises:

Indicate the inverses of the following functions, and then state whether or not they are functions.

a) $ƒ(x) = 2x + 7$

b) $h(x) = 3x^2 - 5x + 1$

c) $j(x) = sqrt(2x - 4) + 5$

d) $k(x) = (3x - 2)/(5x + 4)$

$2.$ The following graph is of function $ƒ^(-1)(x)$ . State the equation of $ƒ(x)$

graph{y = 1/3x + 2 [-9.51, 9.51, -4.755, 4.755]}

Good luck!

How do you find the inverse of h(X)= 5 / (2x + 3)h(X)=52x+3h(X)= 5 / (2x + 3) and is it a function?