Let h(x)=x g(x) where g is the inverse of f(x). Also the values of f(x) and f prime(x) are given as then the value of h prime(5) equals

Question

Let h(x)=x g(x) where g is the inverse of f(x). Also the values of f(x) and f prime(x) are given as <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/f031ce49c53c7788c4855338b925d145-.png" /> then the value of h prime(5) equals (A) (11/2) (B) (9/2) (C) 5 (D) (5/2)

Tardigrade Admin · Accepted Answer

h prime(5)=5 g prime(5)+g(5)=5 ⋅ (1/f prime(3))+g(5)=(5/2)+3=(11/2)

Q. Let $h (x) = xg (x)$ where $g$ is the inverse of $f (x)$ . Also the values of $f (x)$ and $f^{'} (x)$ are given as

then the value of $h^{'} (5)$ equals

$\frac{11}{2}$

$\frac{9}{2}$

5

$\frac{5}{2}$

$h^{'} (5) = 5 g^{'} (5) + g (5) = 5 \cdot \frac{1}{f ^{'} ( 3 )} + g (5) = \frac{5}{2} + 3 = \frac{11}{2}$

Q. Let h(x)=xg(x) where g is the inverse of f(x). Also the values of f(x) and f′(x) are given as then the value of h′(5) equals

211​

29​

5

25​

h′(5)=5g′(5)+g(5)=5⋅f′(3)1​+g(5)=25​+3=211​

Q. Let $h (x) = xg (x)$ where $g$ is the inverse of $f (x)$ . Also the values of $f (x)$ and $f^{'} (x)$ are given as

then the value of $h^{'} (5)$ equals

$\frac{11}{2}$

$\frac{9}{2}$

$\frac{5}{2}$

$h^{'} (5) = 5 g^{'} (5) + g (5) = 5 \cdot \frac{1}{f ^{'} ( 3 )} + g (5) = \frac{5}{2} + 3 = \frac{11}{2}$