Let $f(x)=7x+5$ and $g(x)=x-1$. If $h(x)=f(g(x))$, then what is the inverse of $h(x)$?
+9466 f(x) = 7x + 5
g(x) = x - 1
h(x) = f( g(x) ) = f( x - 1 ) = 7(x - 1) + 5 = 7x - 7 + 5 = 7x - 2
h(x) = 7x - 2
To find the inverse, let's replace h(x) with y .
y = 7x - 2
Solve for x ....add 2 to both sides of the equation.
y + 2 = 7x
Divide both sides by 7 .
(y + 2)/7 = x
x = (y + 2)/7 So the inverse of h(x) is..
h-1(x) = (x + 2)/7
+9466 f(x) = 7x + 5
g(x) = x - 1
h(x) = f( g(x) ) = f( x - 1 ) = 7(x - 1) + 5 = 7x - 7 + 5 = 7x - 2
h(x) = 7x - 2
To find the inverse, let's replace h(x) with y .
y = 7x - 2
Solve for x ....add 2 to both sides of the equation.
y + 2 = 7x
Divide both sides by 7 .
(y + 2)/7 = x
x = (y + 2)/7 So the inverse of h(x) is..
h-1(x) = (x + 2)/7
