Question

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

Answer 1

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