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Dmitriy789 [7]
3 years ago
14

Find

id="TexFormula1" title="f^-1 ( x ) when f ( x ) = \frac{3x}{x-2}" alt="f^-1 ( x ) when f ( x ) = \frac{3x}{x-2}" align="absmiddle" class="latex-formula">
Mathematics
1 answer:
Usimov [2.4K]3 years ago
4 0

f^{-1}(x) = \frac{2x}{x-3}

let y = f(x), then rearrange making x the subject

y = \frac{3x}{x-2} ( multiply both sides by (x - 2 ))

y(x - 2 ) = 3x (distribute )

xy - 2y = 3x ( subtract 3x and add 2y to both sides )

xy - 3x = 2y (factor out x on left side )

x(y - 3 ) = 2y ( divide both sides by (y - 3) )

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

change y to x for inverse function

f^{-1}(x) = \frac{2x}{x-3}



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