If f(x) and g(x) are two functions with g(x) = x-(1/x) and fog(x) = x3- (1/x3) then f'(x) = is:

Question

If f(x) and g(x) are two functions with g(x) = x-(1/x) and fog(x) = x3- (1/x3) then f'(x) = is: (A) 3x2+ (3/x4) (B) 1+ (1/x2) (C) x2+ (1/x2) (D) 3x2+3

Tardigrade Admin · Accepted Answer

We have, g(x)=x-(1/x) and f o g(x)=x3-(1/x3) ⇒ f g(x) =(x-(1/x))3+3(x-(1/x)) As g(x)=x-(1/x) (given) ∴ f(x-(1/x))=(x-(1/x))3+3(x-(1/x)) Let x-(1/x)=t ⇒ f(t)=t3+3 t ⇒ f(x)=x3+3 x ⇒ f'(x)=3 x2+3

Q. If $f (x)$ and $g (x)$ are two functions with $g (x) = x - \frac{1}{x}$ and $f o g (x)$ = $x^{3} - \frac{1}{x ^{3}}$ then $f^{'} (x) =$ is:

$3 x^{2} + \frac{3}{x ^{4}}$

$1 + \frac{1}{x ^{2}}$

$x^{2} + \frac{1}{x ^{2}}$

$3 x^{2} + 3$

Q. If f(x) and g(x) are two functions with g(x)=x−x1​ and fog(x) = x3−x31​ then f′(x)= is:

3x2+x43​

1+x21​

x2+x21​

3x2+3

We have, g(x)=x−x1​ and fog(x)=x3−x31​ ⇒f{g(x)}=(x−x1​)3+3(x−x1​) As g(x)=x−x1​ (given) ∴f(x−x1​)=(x−x1​)3+3(x−x1​) Let x−x1​=t ⇒f(t)=t3+3t ⇒f(x)=x3+3x ⇒f′(x)=3x2+3

Q. If $f (x)$ and $g (x)$ are two functions with $g (x) = x - \frac{1}{x}$ and $f o g (x)$ = $x^{3} - \frac{1}{x ^{3}}$ then $f^{'} (x) =$ is:

$3 x^{2} + \frac{3}{x ^{4}}$

$1 + \frac{1}{x ^{2}}$

$x^{2} + \frac{1}{x ^{2}}$

$3 x^{2} + 3$