Question

What is the inverse of the function g(x)=-\dfrac{2}{3}x-5g(x)=− 3 2 ​ x−5g, left parenthesis, x, right parenthesis, equals, minus, start fraction, 2, divided by, 3, end fraction, x, minus, 5?

Answer 1

Answer:

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

Step-by-step explanation:

Given function,

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

Step 1 : Replace g(x) by y:

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

Step 2 : Swap x and y:

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

Step 3 : Solve the equation for y ( isolate y in the left side ):

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

     $\frac{2}{3}y=-5-x$

      $y=\frac{3}{2}(-5-x)$

      $y=-\frac{15}{2}-\frac{3}{2}x$

      $y=-\frac{3}{2}x-\frac{15}{2}$

Step 4: Replace y by $g^{-1}(x)$:

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

Hence, the inverse of the function g(x) is $g^{-1}(x)=-\frac{3}{2}x-\frac{15}{2}$.