Answer:
[tex]f^{-1}[/tex](x) = ( [tex]\frac{9x-1}{8}[/tex] )²
Step-by-step explanation:
f(x) = [tex]\frac{8\sqrt{x} +1}{9}[/tex]
y = [tex]\frac{8\sqrt{x} +1}{9}[/tex]
Solve equation for x
8√x + 1 = 9y
8√x = 9y - 1
√x = [tex]\frac{9y-1}{8}[/tex]
(√x)² = ( [tex]\frac{9y-1}{8}[/tex] )²
x = ( [tex]\frac{9y-1}{8}[/tex] )²
Switch "x" and "y"
y = ( [tex]\frac{9x-1}{8}[/tex] )²
[tex]f^{-1}[/tex](x) = ( [tex]\frac{9x-1}{8}[/tex] )²
