Find f1x for the function fx 3x 7 Find g1x for the functio

Find f^-1(x) for the function. f(x) = 3x - 7 Find g^-1(x) for the function. G(x) = 4x - 3/x - 5

Solution

(a) Let y = f(x) = 3x -7 . Then 3x = y +7 so that x = (y+7)/3. Now, on interchanging x and y, we get y = (x+7)/3 so that f^-1(x) = (x +7)/3

(b) Let y = g(x) = (4x-3)/(x-5). Then y(x-5) = 4x -3 or, xy -5y = 4x -3 or, 4x –xy = 3-5y or, x( 4-y) = (3-5y) so that x = (3-5y)/(4-y). Now, on interchanging x and y, we get y = (3-5x)/(4 –x) so that g^-1(x) = (3-5x)/(4 –x)