Question

What is the inverse of the function g(x)=-2/3x-5

Answer 1

Answer:

$f^-^1(x) = -\frac{3}{2}x - \frac{15}{2}$

Step-by-step explanation:

Step 1:  Set x to y and y to x

$y = -2/3x - 5$

$x = -2/3y - 5$

Step 2:  Solve for y

$x + 5 = -2/3y - 5 + 5$

$x + 5 = -2/3y$

$-3/2(x + 5) = -2/3y * -3/2$

$-3/2x - 15/2 = y$

Step 3:  Make new equation

$f^-^1(x) = -\frac{3}{2}x - \frac{15}{2}$

Answer:  $f^-^1(x) = -\frac{3}{2}x - \frac{15}{2}$

Answer 2

Answer:

-3/2x -15/2

Step-by-step explanation:

g(x)=-2/3x-5

y = -2/3x -5

Exchange x and y

x = -2/3y -5

Solve for y

Add 5 to each side

x+5 = -2/3y-5+5

x+5 = -2/3y

Multiply each side by -3/2

-3/2(x+5) =-3/2*-2/3y

-3/2x -15/2 =y

The inverse is -3/2x -15/2