Question

If f(x)=4/x+2 and g is the inverse of f,then g'(10)=​

Answer 1

g'(10) =
`(-1)/(16)`

Step-by-step explanation:

Since g is the inverse of f ,

We can write

g(f(x)) = x (Identity)

Differentiating both sides of the equation we get,

g'(f(x)).f'(x) = 1

g'(10) =
`(1)/(f'(x))` --equation[1] Where f(x) = 10

Now, we have to find x when f(x) = 10

Thus 10 =
`(4)/(x)` + 2

`(4)/(x)` = 8

x =
`(1)/(2)`

Since f(x) =
`(4)/(x)` + 2

f'(x) = -
`(4)/(x^(2) )`

f'(
`(1)/(2)`) = -4 × 4 = -16

Putting it in equation 1, we get:

We get g'(10) = -
`(1)/(16)`