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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

Respuesta :

VirαtKσhli

Answer:

[tex]\boxed{\red{\sf h^{-1}(x)=\dfrac{4}{3}x+22}}[/tex]

Step-by-step 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 ,

[tex]:\implies[/tex] h(x) = 3/2 ( x -11)

[tex]:\implies[/tex] y = 3/2 ( x - 11)

[tex]:\implies[/tex] y = 3/2x - 33/2

  • Now replace x and y.

[tex]:\implies[/tex] x = 3/2y - 33/2

  • Now solve out for y .

[tex]:\implies[/tex] x + 33/2 = y × 3/2

[tex]:\implies[/tex] y = (2x + 33)×2/3

[tex]:\implies[/tex] y = 4x/3 + 22

  • Replacing y with h-¹(x)

[tex]:\implies[/tex] h-¹(x) = 4x/3 + 22

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

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