Question

What's the inverse of this function

`f(x) = (2)/(3) x - 2`
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Answer 1

`\displaystyle{f^(-1)(x) = (3)/(2)x+3}`

Explanation:

Let y = f(x):

`\displaystyle{y=(2)/(3)x-2}`

Swap x and y:

`\displaystyle{x=(2)/(3)y-2}`

Solve for y:

`\displaystyle{x\cdot 3=(2)/(3)y\cdot 3-2\cdot 3}\\\\\displaystyle{3x=2y-6}\\\\\displaystyle{3x+6=2y}\\\\\displaystyle{y=(3x+6)/(2)}\\\\\displaystyle{y=(3)/(2)x+(6)/(2)}\\\\\displaystyle{y=(3)/(2)x+3}`

Hence, the inverse is:

`\displaystyle{f^(-1)(x) = (3)/(2)x+3}`