Question

yay. pahelp nga po..
Find the inverse function of x= (4-3y)^(3/2)

Answer 1

The function can be written like this :
\[\Large f(y)=(4-3y)^{\frac32}=\sqrt{(4-3y)^3}\]
To find the inverse function, we solve the equation f(y)=x.
We have :
\[\Large f(y)=x\iff \sqrt{(4-3y)^3}=x\iff (4-3y)^3=x^2\]
\[\Large ~~\iff 4-3y=\sqrt[3]{x^2}\iff 3y=4-\sqrt[3]{x^2}\iff y=\frac{4-\sqrt[3]{x^2}}{3}\]
So, the inverse function is :
\[\Large f^{-1}(x)=\frac{4-\sqrt[3]{x^2}}{3}\]