Question

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

Answer 1

Answer:

The value of g'(10)=$\frac{(-1)}{16}$

Step-by-step explanation:

Given function is f(x)=$\frac{4}{x} + 2$

Take f(x)=y

y=$\frac{4}{x} + 2$

Subtract 2 from both side.

y-2=$\frac{4}{x}$

x=$\frac{4}{y-2}$

The inverse of f(x) is written as $\frac{4}{y-2}$

It is said as g is inverse of f

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

g(y)=$\frac{4}{y-2}$

g(10)=$\frac{4}{10-2}$

g(10)=$\frac{1}{2}$

Differentiating both sides we get,

g'(y)=$\frac{4(-1)}{(y-2)^{2}}+0$

g'(y)=$\frac{(-4)}{(y-2)^{2}}$

To find g'(10)=$\frac{(-4)}{(10-2)^{2}}$

g'(10)=$\frac{(-1)}{16}$