[tex]f(x) = \frac{2x + 1}{3x - 4}[/tex]
h(x) = 3x³ - 7
[tex]f(x) = \frac{2x + 1}{3x - 4}[/tex]
[tex]y = \frac{2x + 1}{3x - 4}[/tex]
[tex]y(3x - 4) = (3x - 4)(\frac{2x + 1}{3x - 4})[/tex]
[tex]y(3x) - y(4) = 2x + 1[/tex]
[tex]3xy - 4y = 2x + 1[/tex]
[tex]3xy - 2x = 4y + 1[/tex]
[tex]x(3y) - x(2) = 4y + 1[/tex]
[tex]x(3y - 2) = 4y + 1[/tex]
[tex]\frac{x(3y - 2)}{3y - 2} = \frac{4y + 1}{3y - 2}[/tex]
[tex]x = \frac{4y + 1}{3y - 2}[/tex]
[tex]y = \frac{4x + 1}{3x - 2}[/tex]
[tex]f^{-1}(x) = \frac{4x + 1}{3x - 2}[/tex]
f(h(4)) = 3x³ - 7
f(h(4)) = 3(4)³ - 7
f(h(4)) = 3(64) - 7
f(h(4)) = 192 - 7
f(h(4)) = 185
[tex]f^{-1}(x) - f(h(4)) =\frac{4x + 1}{3x - 2} - 185[/tex]
[tex]f^{-1}(x) - f(h(4)) =\frac{4x + 1}{3x - 2} = \frac{185(3x - 2)}{3x - 2}[/tex]
[tex]f^{1}(x) - f(h(4)) =\frac{4x + 1}{3x - 2} = \frac{555x - 370}{3x - 2}[/tex]
[tex]f^{-1}(x) - f(h(4)) =\frac{(4x + 1) - (555x - 370)}{3x - 2}[/tex]
[tex]\f^{-1}(x) - f(h(4)) =\frac{(4x - 555x) + (1 - 370)}{3x - 2}[/tex]
[tex]f^{-1}(x) - f(h(4)) =\frac{-551x - 369}{3x - 2}[/tex]
