Question

Find the inverse function of h(x) = -2/3x + 6.

Answer 1

Answer:

$x=-\frac{3}{2} x+9$

Step-by-step explanation:

We are given the following function and we are to find the inverse of this function:

$h(x) = - \frac { 2 } { 3 } x + 6$

For that, we will put the function equal to another variable $y$ and make $x$ the subject of the function.

$y = - \frac { 2 } { 3 } x + 6$

Making $x$ the subject:

$y-6=-\frac{2}{3} x$

$3(y-6)=-2x$

$\frac{3y-18}{-2} =x$

$x=-\frac{3}{2} x+9$

Therefore, the inverse h'(x) = $x=-\frac{3}{2} x+9$.

Answer 2

Answer:

$h^{-1}(x)=-\frac{3}{2}x+9$

Step-by-step explanation:

To find inverse of a function, follow the steps below:

1. replace h(x) with y

2. Interchange x and y

3. Solve for the new y

4. Replace y to $h^{-1}(x)$ (this is the inverse function)

Step 1: y = -2/3x+6

Step 2: x = -2/3y+6

Step 3:

$x=-\frac{2}{3}y+6\\\frac{2}{3}y=-x+6\\y=\frac{-x}{\frac{2}{3}}+\frac{6}{\frac{2}{3}}\\y=-\frac{3}{2}x+9$

Step 4:

$y=-\frac{3}{2}x+9\\h^{-1}(x)=-\frac{3}{2}x+9$

This is the inverse function.