Question

What is the 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?
h^{-1}(x)=h
−1
(x)=h, start superscript, minus, 1, end superscript, left parenthesis, x, right parenthesis, equals

Answer 1

`\boxed{\red{\sf h^(-1)(x)=(4)/(3)x+22}}`

Explanation:

Given :-

• h(x) = 3/2 ( x - 11)

And we need to find the Inverse of the function . So for that firstly replace h(x) with y , we have ,

`:\implies` h(x) = 3/2 ( x -11)

`:\implies` y = 3/2 ( x - 11)

`:\implies` y = 3/2x - 33/2

• Now replace x and y.

`:\implies` x = 3/2y - 33/2

• Now solve out for y .

`:\implies` x + 33/2 = y × 3/2

`:\implies` y = (2x + 33)×2/3

`:\implies` y = 4x/3 + 22

• Replacing y with h-¹(x)

`:\implies` h-¹(x) = 4x/3 + 22

Hence the inverse of the function is 4x/3 + 22