Question

Given the function f(x) = 5(x+4) − 6, solve for the inverse function when x = 19.

Answer 1

If f(x) = 5(x + 4) - 6
then y = 5(x + 4) - 6

By interchanging x & y
⇒ x = 5(y + 4) - 6

⇒
`(x + 6)/(5)` = y + 4

⇒ y =
`(x - 14)/(5)`

∴ f⁻¹(x) =
`(x - 14)/(5)`

When x = 19 ;

f⁻¹(19) =
`(19 - 14)/(5)`
= 1

∴ when x= 19 the inverse is equal to 1.

Answer 2

F(x)=y=5(x+4)-6
f^(-1)(x)=x=5(y+4)-6
x+6=5(y+4)
(1/5)x+(6/5)=y+4
(1/5)(x)+(6/5)-4=y
y=0.2x-2.8
0.2(19)-2.8
3.8-2.8=1
f^(-1)(19)=1