given fx find f1x by using the xy interchange method fx 5x23

given f(x), find f^-1(x) by using the x-y interchange method.

f(x)= 5(x-2)^³+9

Solution

f(x) = 5( x-2)^3 +9

Plug x = y and y =x

y =5( x-2)^3 +9

x= 5(y -2)^3 +9

(x -9) = 5(y -2)^3

y- 2 = [(x -9)/5]^1/3

y = 2 + [(x -9)/5]^1/3

f^-1(x) = 2 + [(x -9)/5]^1/3