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

⇒  $\frac{x + 6}{5}$ = y + 4 

⇒  y = $\frac{x - 14}{5}$

∴ f⁻¹(x) = $\frac{x - 14}{5}$

When  x = 19 ; 

f⁻¹(19) = $\frac{19 - 14}{5}$
           = 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