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What's the inverse of this function

f(x) = (2)/(3) x - 2


User Weisjohn
by
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1 Answer

3 votes

Answer:


\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}

User Tgriesser
by
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