In each let y = f(x) and rearrange making x the subject
(7)
y = 3x + 9 ( subtract 9 from both sides )
3x = y - 9 ( divide both sides by 3 )
x = [tex]\frac{y-9}{3}[/tex]
change y back into terms of x
[tex]f^{-1}[/tex](x) = [tex]\frac{x-9}{3}[/tex]
(8)
y = 5x - 2
5x = y + 2 ( divide both sides by 5 )
x = [tex]\frac{y+2}{5}[/tex]
[tex]f^{-1}[/tex](x) = [tex]\frac{x+2}{5}[/tex]
(9)
y = - x + 2
x = 2 - y
[tex]f^{-1}[/tex](x) = 2 - x
(10)
y = - 4x + 3
4x = 3 - y ( divide both sides by 4 )
x = [tex]\frac{3-y}{4}[/tex]
[tex]f^{-1}[/tex](x) = [tex]\frac{3-x}{4}[/tex]
(11)
y = 0.5x - 2
0.5x = y + 2 ( divide both sides by 0.5 )
x = 2(y + 2)
[tex]f^{-1}[/tex](x) = 2x + 4
(12)
y = - 0.25x + 6
0.25x = 6 - y ( divide both sides by 0.25 )
x = 4(6 - y )
[tex]f^{-1}[/tex](x) = 24 - 4x
