Question #308099

(a) Find the derivative of the function 𝑦 = 2𝑥^2+12/x^2, when 𝑥 = 2.

(b) Let 𝑓(𝑥) = −3/𝑥−7. Find the inverse of the function.


1
Expert's answer
2022-03-11T12:47:50-0500

Solution (a)

𝑦=2𝑥2+12x2𝑦 = 2𝑥^2+\frac{12}{x^2}


𝑦=2𝑥2+12x2𝑦 = 2𝑥^2+12x^{-2}


dydx=(2)(2)𝑥21+(12)(2)x21\frac{dy}{dx}= (2)(2)𝑥^{2-1}+(12)(-2)x^{{-2-1}}


dydx=4𝑥24x3\frac{dy}{dx}= 4𝑥-24x^{-3}


at the point x=2x=2


dydx=4(2)(24)(2)3\frac{dy}{dx}= 4(2)-(24)(2)^{-3}


dydx=12248\frac{dy}{dx}= 12-\frac{24}{8}


dydx=9\frac{dy}{dx}= 9


Hence the derivative of 𝑦=2𝑥2+12/x2𝑦 = 2𝑥^2+12/x^2, when 𝑥=2𝑥 = 2 is


dydx=9\frac{dy}{dx}= 9




Solution (b)


Given that 𝑓(𝑥)=y=3x7𝑓(𝑥) =y= -\frac{3}{x-7} .


Interchanging xx (domain) and yy (range)


x=3y7x= -\frac{3}{y-7}


Now making yy the subject of the formula, we have


x(y7)=3x(y-7)=-3


y7=3xy-7=-\frac{3}{x}


y=3x+7y=-\frac{3}{x}+7


Hence the inverse function of the given function 𝑓(𝑥)=y=3x7𝑓(𝑥) =y= -\frac{3}{x-7} is


𝑓1(𝑥)=3x+7𝑓^{-1}(𝑥) =-\frac{3}{x}+7





Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!
LATEST TUTORIALS
APPROVED BY CLIENTS