Exercise 16 Page 268

Before we can find the inverse of the given function, we need to replace f(x) with y. f(x)=4(x+17) ⇔ y=4(x+17) Now, to algebraically determine the inverse of the given equation, we exchange x and y and solve for y. Given Equation & Inverse Equation y=4( x+17) & x=4( y+17) The result of isolating y in the new equation will be the inverse of the given function.

x=4(y+17)

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Solve for y

DivEqn

.LHS /4.=.RHS /4.

x/4=y+17

MoveNumRight

a/b=1/b* a

1/4x=y+17

SubEqn

LHS-17=RHS-17

1/4x-17=y

RearrangeEqn

Rearrange equation

y= 1/4x-17

Finally, we write the inverse of the given function in function notation by replacing y with f^(- 1)(x) in our new equation. f^(- 1)(x)=1/4x-17