The onetoone function h is defined below hx 7x 88x 3 Find

The one-to-one function h is defined below. h(x) = 7x- 8/8x + 3 Find h^-1(x), where h^-1 is the inverse of h. Also state the domain and range of h^-1 in interval notation. h^-1 (x) = Domain of h^-1: Range of h^-1:

Solution

Solution:

Here;

h(x) = (7x-8) / (8x+3)

=> 8x h(x) + 3h(x) = 7x-8

=> x(8h(x)-7) = -8 -3h(x)

=> x = (8+3h(x)) / (7-8h(x))

=> h^-1(x) = (8+3x) / (7-8x)

Domain: x (-,7/8) U (7/8,+)

Range: h^-1(x) (-,+)