Question

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

Answer 1

Answer:

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

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) = $\frac{1}{f'(x)}$    --equation[1]    Where f(x) = 10

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

Thus 10 = $\frac{4}{x}$ + 2

$\frac{4}{x}$ = 8

x = $\frac{1}{2}$

Since f(x) = $\frac{4}{x}$ + 2

f'(x) = -$\frac{4}{x^{2} }$

f'($\frac{1}{2}$)  =  -4 × 4 = -16            

Putting it in equation 1, we get:

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