mbjj1381 mbjj1381
  • 26-01-2022
  • Mathematics
contestada

Let f be the function defined by f(x)=x3 x. If g(x)=f−1(x) and g(2)=1, what is the value of g′(2)?.

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Tanitoluwasoubi
Tanitoluwasoubi Tanitoluwasoubi
  • 26-01-2022

Answer:

1/6

Step-by-step explanation:

Given the function

f(x)=x^3+x^2+x

Get the inverse. Let y = f(x)

y = x^3+x^2+x

Replace y with x

x = y³+y²+y

Differentiate with respect to x

1 =3y²dy/dx + 2ydy/dx + dy/dx

1 = (3y²+2y+1)dy/dx

dy/dx = 1/3y²+2y+1

g'(x) = 1/3(g(x))²+2g(x)+1

If x = 3

g'(3) = 1/3(g(3))²+2g(3)+1

g'(3) =1/3(1)²+2(1)+1

g'(3) = 1/3+2+1

g'(3) = 1/6

Hence g'(3) = 1/6

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