Question

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

tentukan :
A. infers fungsi F
B. Nilai dari f^-1 (-3)​​

Answer 1

The answer are

A.

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

B.

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

Explanation:

To find the infers we do that

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