Question

IM TAKING AN EXAM AND I NEED SO MUCH HELP!!

Answer 1

Answer:

$f^{-1}(x) = \sqrt[3]{x+5}$

Step-by-step explanation:

A function $f^{-1}$ is the inverse of f if whenever y =f(x) and $x =f^{-1}$

To find the  inverse of f(x) = $x^{3}$ - 5, we use the following steps:

• Step 1 : Put y for f(x) and solve for x

y = $x^{3}$ - 5

<=> $x^{3}$  = y + 5

<=> x = $\sqrt[3]{y+ 5}$

• Step 2: Put $f^{-1}(y)$ for x, we have:

$f^{-1}(y) =\sqrt[3]{y+5}$

• Step 3: Interchange y =x, we have

$f^{-1}(x) = \sqrt[3]{x+5}$

Let Calculate 3 points on f(x)

x = 0 => y = -5

x = 1  => y = -4

x = 2 => y = 3

Let Calculate 3 points on $f^{-1}$ (x)

x = -5 => y = 0

x = -4  => y = 1

x = 3 => y = 2

Yes, the inverse is correct because:

• the domain of the inverse function is the range of the original function

• the range of the inverse function is the domain of the original function