Need help on this one please hurry

Question

asked May 25, 2024 92.6k views

1 Answer

Shantanu Banerjee · Answer 1 · 2024-06-01T08:41:11+0000

Answer: The answer is F

Explanation:

To figure out if it is equal, you can use the second equation to check and see what the new function will be when you solve it

Second Equation:
f(x)=(x-3)^3+4

Steps:

1. Substitute y for f(x):
y=(x-3)^3+4

2. Interchange x and y:
x=(y-3)^3+4

3. Swap sides of the equation:
(y-3)^3+4=x

4. Move constant to the right and change sign:
(y-3)^3=x-4

5. Take the root of both sides of equation:
$y-3=\sqrt[3]{x-4}$

6. Move constant to right and change sign again:
$y=\sqrt[3]{x-4} +3$

7. Substitute
f^(-1)(x) for
to get answer:
$f^(-1)(x)=\sqrt[3]{x-4}+3$

This answer is False because the the numbers in this equation we just checked (-4 and +3) are not the same as the first equation

$f^(-1)(x)=-3 +\sqrt[3]{x+4}$ where the signs are flipped (+4 and -3)