Exercise 15 Page 268

Before we can find the inverse of the given function, we need to replace f(x) with y. f(x)=17-1/3x ⇔ y=17-1/3x Now, to algebraically determine the inverse of the given equation, we exchange x and y and solve for y. Given Equation & Inverse Equation y=17-1/3 x & x=17-1/3 y The result of isolating y in the new equation will be the inverse of the given function.

x=17-1/3y

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Solve for y

SubEqn

LHS-17=RHS-17

x-17=-1/3y

MultEqn

LHS * (- 3)=RHS* (- 3)

- 3(x-17)=y

Distr

Distribute - 3

- 3x+51=y

RearrangeEqn

Rearrange equation

y= - 3x+51

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)=- 3x+51