Answer:
[tex]f^{-1}[/tex](x) = [tex]\frac{3x-15}{2}[/tex]
Step-by-step explanation:
Given
y = [tex]\frac{2}{3}[/tex] x + 5
Rearrange making x the subject
Multiply through by 3 to clear the fraction
3y = 2x + 15 ( subtract 15 from both sides )
3y - 15 = 2x ( divide both sides by 2 )
[tex]\frac{3y-15}{2}[/tex] = x
Replace x by [tex]f^{-1}[/tex] (x) and y by x, thus
[tex]f^{-1}[/tex] (x) = [tex]\frac{3x-15}{2}[/tex]
