Question

F(x)= 2x+1/3x-4 H(x)=3x³-7 Evaluate F(x)–¹ And Fh(4)

Answer 1

`f(x) = (2x + 1)/(3x - 4)`
h(x) = 3x³ - 7


`f(x) = (2x + 1)/(3x - 4)`

`y = (2x + 1)/(3x - 4)`

`y(3x - 4) = (3x - 4)((2x + 1)/(3x - 4))`

`y(3x) - y(4) = 2x + 1`

`3xy - 4y = 2x + 1`

`3xy - 2x = 4y + 1`

`x(3y) - x(2) = 4y + 1`

`x(3y - 2) = 4y + 1`

`(x(3y - 2))/(3y - 2) = (4y + 1)/(3y - 2)`

`x = (4y + 1)/(3y - 2)`

`y = (4x + 1)/(3x - 2)`

`f^(-1)(x) = (4x + 1)/(3x - 2)`

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


`f^(-1)(x) - f(h(4)) =(4x + 1)/(3x - 2) - 185`

`f^(-1)(x) - f(h(4)) =(4x + 1)/(3x - 2) = (185(3x - 2))/(3x - 2)`

`f^(1)(x) - f(h(4)) =(4x + 1)/(3x - 2) = (555x - 370)/(3x - 2)`

`f^(-1)(x) - f(h(4)) =((4x + 1) - (555x - 370))/(3x - 2)`

`\f^(-1)(x) - f(h(4)) =((4x - 555x) + (1 - 370))/(3x - 2)`

`f^(-1)(x) - f(h(4)) =(-551x - 369)/(3x - 2)`