Question

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

Answer 1

The value of g'(10)=
`((-1))/(16)`

Explanation:

Given function is f(x)=
`(4)/(x) + 2`

Take f(x)=y

y=
`(4)/(x) + 2`

Subtract 2 from both side.

y-2=
`(4)/(x)`

x=
`(4)/(y-2)`

The inverse of f(x) is written as
`(4)/(y-2)`

It is said as g is inverse of f

g(y)=\frac{4}{y-2}[/tex]

g(y)=
`(4)/(y-2)`

g(10)=
`(4)/(10-2)`

g(10)=
`(1)/(2)`

Differentiating both sides we get,

g'(y)=
`(4(-1))/((y-2)^(2))+0`

g'(y)=
`((-4))/((y-2)^(2))`

To find g'(10)=
`((-4))/((10-2)^(2))`

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