Question

Inverse of the function h(x)=\dfrac{3}{2}(x-11)h(x)= 2 3 ​ (x−11)h, left parenthesis, x, right parenthesis, equals, start fraction, 3, divided by, 2, end fraction, left parenthesis, x, minus, 11, right parenthesis?

Answer 1

Answer:

$h^{-1}(x)=\frac{2}{3}x+11$

Step-by-step explanation:

The given function is

$h(x)=\dfrac{3}{2}(x-11)$

We need to find the inverse of the given function.

Step 1: Substitute h(x)=y.

$y=\dfrac{3}{2}(x-11)$

Step 2: Interchange x and y.

$x=\dfrac{3}{2}(y-11)$

Step 3: Isolate y.

$\frac{2}{3}x=y-11$

$\frac{2}{3}x+11=y$

Step 4: Interchange sides.

$y=\frac{2}{3}x+11$

Step 5: Substitute $y=h^{-1}(x)$.

$h^{-1}(x)=\frac{2}{3}x+11$

Therefore, the inverse of the function is $h^{-1}(x)=\frac{2}{3}x+11$.

Answer 2

Answer:

The inverse function of h(x) = 3/2*(X-11)  is:  g(x)= (2/3*X) +11

Step-by-step explanation:

h(x) = Y= 3/2*(X-11)

To find the inverse function, the first step is to exchange the position of the variables with each other. So;

X= 3/2*(Y-11)

Now we need to isolate the variable Y from this equation. The final result will be te inverse function.

X=3/2*(Y-11)

2*X=3*(Y-11)

2/3*X=Y-11

2/3*X +11 = Y

Y= (2/3*X) + 11  (Inverse function)