Respuesta :

TaeKwonDoIsDead

Answer:

[tex]h^{-1}(x)=-\frac{3}{2}x+9[/tex]

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 [tex]h^{-1}(x)[/tex] (this is the inverse function)

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

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

Step 3:

[tex]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[/tex]

Step 4:

[tex]y=-\frac{3}{2}x+9\\h^{-1}(x)=-\frac{3}{2}x+9[/tex]

This is the inverse function.

alinakincsem

Answer:

[tex]x=-\frac{3}{2} x+9[/tex]

Step-by-step explanation:

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

[tex] h(x) = - \frac { 2 } { 3 } x + 6 [/tex]

For that, we will put the function equal to another variable [tex]y[/tex] and make [tex]x[/tex] the subject of the function.

[tex] y = - \frac { 2 } { 3 } x + 6 [/tex]

Making [tex]x[/tex] the subject:

[tex]y-6=-\frac{2}{3} x[/tex]

[tex]3(y-6)=-2x[/tex]

[tex]\frac{3y-18}{-2} =x[/tex]

[tex]x=-\frac{3}{2} x+9[/tex]

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

Otras preguntas