Question

Find the inverse f(x)=3√(x-7)-9

Answer 1

Is -9 inside the square root or outside?

Answer 2

sorry its x/7 and to be clear is not the square root its the square root with the 3 in it

Answer 3

outside the square root

Answer 4

\[\Large f(x) = \sqrt[3]{\frac{ x }{ 7 }} - 9\]
Is that the function?

Answer 5

yes thats it

Answer 6

Okay. f(x) is same as y.
So put y in the place of f(x)
\[\Large y = \sqrt[3]{\frac{ x }{ 7 }} - 9\]

Answer 7

To find the inverse, first interchange x and y. That is, replace y with x and x with y.\[\Large x = \sqrt[3]{\frac{ y }{ 7 }} - 9\]Now solve for y. Can you do that?

Answer 8

Isolate y by adding 9 to both sides.
Then cube both sides. The cube and the cube root will cancel each other on the right. Tell me what you get.

Answer 9

cuberoot of (x+9)= y/7 right

Answer 10

Not cuberoot but CUBE. We are cubing both sides. The left side will be (x+9)^3 and the right side will be y/7

Answer 11

ok so (x+9)^3=y/7 if im still trying to isolate y do i divide everything by 7?

Answer 12

Multiply both sides by 7

Answer 13

What do you get?

Answer 14

(7x+63)^3=y ?

Answer 15

No need to take the 7 inside. You can leave it as a factor outside:
7(x + 9)^3 = y
Switch the right and left sides:
y = 7(x + 9)^3

That is your inverse function.

Answer 16

thank you for the help!

Answer 17

You are welcome.