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liberstina [14]
3 years ago
8

F(x)= 2x+3/x-1, x ≠ 1, dan f^-1 adalah invers dari f

Mathematics
1 answer:
Sindrei [870]3 years ago
5 0

Answer:

The answer are

A.

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

B.

{f}^{ - 1} ( - 3) = 0

Step-by-step explanation:

To find the infers we do that

f(x) =  \frac{2 x + 3}{x - 1 }  \\ (x - 1)f(x) = 2x + 3 \\ xf(x) - f(x) = 2x + 3 \\ xf(x) - 2x = f(x) + 3 \\ x(f(x) - 2) = f(x) + 3 \\  x =  \frac{f(x) + 3}{f(x) - 2}  \\ then \:  \\  {f}^{ - 1} (x) =  \frac{x + 3}{x - 2}  \\ then \\  {f }^{ - 1} ( - 3) =  \frac{ - 3 + 3}{ - 3 + 2}  = 0

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