Manipulating Radical Functions

f (x),

we first need to replace

f (x)

with

y .

From there, we switch

x

and

y

and solve for

y .

y = \frac{3 x}{3} \to x = \frac{3 y}{3}

The resulting equation will be the inverse of the given function.

x = \frac{3 y}{3}

Solve for

y

LHS \cdot 3 = RHS \cdot 3

3 x = 3 y

LHS^{3} = RHS^{3}

(3 x)^{3} = (3 y)^{3}

CalcPowCalculate power

27 x^{3} = (3 y)^{3}

(n a)^{n} = a

27 x^{3} = y

RearrangeEqnRearrange equation

y = 27 x^{3}

Finally, to indicate that this is the inverse function of

f (x),

we will replace

y

with

f^{- 1} (x) .

f^{- 1} (x) = 27 x^{3}

Manipulating Radical Functions 1.13 - Solution