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11/28/11 f (x) = 3x − 5 f −1 (x) = x +5 3 € The function f gives an expression of y in terms of x. To find the inverse of f we need an expression of x in terms of y: ◦ y=f(x) ◦ Solve for x! ◦ Since we usually consider x the independent, and y dependent, we exchange y and x. 1 11/28/11 Find inverse of If a, x>0, and a ≠ 1, the logarithm of x with base a is denoted by logax and is defined as follows: y = loga x loga x if and only if x=ay = exponent needed on base a to get x 2 11/28/11 Since exponential and logarithmic functions are inverse we have: 3 11/28/11 log a x = log b x log b a € 4 11/28/11 5 11/28/11 6 11/28/11 7 11/28/11 8 11/28/11 2[log 4 x − log 4 (x − 2)] = € 9 11/28/11 10 11/28/11 log 9 [(xy) 2 (x + 3) 4 ] = € 11 11/28/11 12 11/28/11 13 11/28/11 14 11/28/11 15