Let fx 93 10x 3 Find f1x where f1 is the inverse function

Let f(x) = 9/3 -10x = 3. Find f^-1(x), where f^-1 is the inverse function of f. Let f(x) = 4x - 1/1 -7x. Find f^-1(x), where f^-1 is the inverse function of f.

Solution

16)     f(x) = 9/(3 -10x) - 3

To find f^-1(x) : plug x= y and y = x, solve for y

y = 9/(3 -10x) - 3

x = 9/(3 -10y) -3

(x+3) = 9/(3- 10y)

3 -10y = 9/(x+3)

10y = 3 - 9 /(x+3)

y = 3/10 - 9/10(x+3)

f^-1(x) = 3/10 - 9/10(x+3)

17)     f(x) = (4x -1)/( 1- 7x)

To find f^-1(x) : plug x= y and y = x, solve for y

y = (4x -1)/( 1- 7x)

x = (4y -1)/(1 - 7y)

x( 1- 7y) = 4y -1

x - 7xy = 4y -1

4y +7xy = x+1

y( 4 + 7x) = (x+1)

y = (x+1)/(4 +7x)

f^-1(x) = (x+1)/(4 +7x)