Given the function f (x) = 6 (x+2) - 3, solve for the inverse function when x = 21.

Inverse, baseically

replace f (x) with y

switch all x and y

solve for y

replace y with f⁻¹ (x)

f (x) = 6 (x+2) - 3

replace with y

y=6 (x+2) - 3

switch x and y

x=6 (y+2) - 3

solve for y

x=6y+12-3

x=6y+9

minus 9

x-9=6y

divide 6

1/6x-3/2=y

replace

f⁻¹ (x) = 1/6x-3/2

when x=21

f⁻¹ (21) = 1/6 (21) - 3/2

f⁻¹ (21) = 21/6-3/2

f⁻¹ (21) = 21/6-9/6

f⁻¹ (21) = 12/6=

f⁻¹ (21) = 2

answer is f⁻¹ (21) = 2

inverse function is

f⁻¹ (x) = 1/6x+3/2