If f(x) and g(x) are two functions with g(x)= | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $g(x)=x-\frac{1}{x}$.We are given $f \circ g(x) = x^3-\frac{1}{x^3}$.We know the algebraic identity $(a-b)^3 = a^3 - b^3 - 3ab(a-b)$,which i

Vedclass · Accepted Answer

$3x^2+3$

Vedclass · Answer

(D) Given $g(x)=x-\frac{1}{x}$.We are given $f \circ g(x) = x^3-\frac{1}{x^3}$.We know the algebraic identity $(a-b)^3 = a^3 - b^3 - 3ab(a-b)$,which implies $a^3-b^3 = (a-b)^3 + 3ab(a-b)$.Substituting $a=x$ and $b=\frac{1}{x}$,we get $x^3-\frac{1}{x^3} = (x-\frac{1}{x})^3 + 3(x)(\frac{1}{x})(x-\frac{1}{x})$.Thus,$f \circ g(x) = (x-\frac{1}{x})^3 + 3(x-\frac{1}{x})$.Since $g(x) = x-\frac{1}{x}$,we can write $f(g(x)) = (g(x))^3 + 3(g(x))$.Replacing $g(x)$ with $x$,we get $f(x) = x^3 + 3x$.Now,differentiating $f(x)$ with respect to $x$,we get $f^{\prime}(x) = \frac{d}{dx}(x^3 + 3x) = 3x^2 + 3$.

If $f(x)$ and $g(x)$ are two functions with $g(x)=x-\frac{1}{x}$ and $f \circ g(x)=x^3-\frac{1}{x^3}$,then $f^{\prime}(x)$ is equal to

Similar Questions

If $f:[-6,6] \rightarrow R$ is defined by $f(x)=x^2-3$ for $x \in R$, then $(f \circ f \circ f)(-1)+(f \circ f \circ f)(0)+(f \circ f \circ f)(1)$ is equal to

If $f: R - \{\frac{3}{7}\} \rightarrow R - \{\frac{3}{7}\}$ is given by $f(x) = \frac{3x+5}{7x-3}$,then the statement which is not true is:

Let $f(x) = x^3$ and $g(x) = 3^x$,then the quadratic equation whose roots are solutions of the equation $(f \circ g)(x) = (g \circ f)(x)$ (for $x \neq 0$) is

If $\phi(x) = x^2 + 1$ and $\psi(x) = 3^x$,then find $\phi \{ \psi(x) \}$ and $\psi \{ \phi(x) \}$.

If $g(f(x)) = |\sin x|$ and $f(g(x)) = (\sin \sqrt{x})^2$,then

Vedclass Test Series

Exam Paper Generator

Online Exam Module