Question

Could someone please explain to me how to solve this equation?

(x-2)^3/4 = 8

Answer 1

@nincompoop Could you help?

Answer 2

\[(x-2)^{\frac{ 3 }{ 4 }}=8\]
Multiply both sides with 4/3 exponent:
\[((x-2)^{\frac{ 3 }{ 4 }})^{\frac{ 4 }{ 3 }}=(8)^{\frac{ 4 }{ 3 }}\]

\[(x-2)=(2)^{4}\]
\[x-2=16\]
x=16+2
x=18

Answer 3

Thank you soo much! I hadn't thought about multiplying by the reciprocal.

Answer 4

you're welcome

Answer 5

Could you help me with one more?

Answer 6

For the function f(x) = (3 - 4x)^2, find f^-1. Also, find whether f^-1 is a function.

I don't know how to deal with f^-1

Answer 7

@jorea143

Answer 8

That's inverse function.

\[f(x) = (3 - 4x)^{2}\]
\[y = (3 - 4x)^{2}\]
Switch x and y:
\[x = (3 - 4y)^{2}\]
then solve for y:
\[\pm \sqrt{x} = \sqrt{(3 - 4y)^{2}}\]
\[\pm \sqrt{x} = 3 - 4y\]
\[4y=3 \pm \sqrt{x}\]
\[y=\frac{3 \pm \sqrt{x}}{4}\]
Change y to \[f^{-1}(x)\]

so
\[f^{-1}(x)=\frac{3 \pm \sqrt{x}}{4}\]

Answer 9

Thank you! I hope you have a good night!

Answer 10

You're welcome. you too