Let f ( x )=2 x ^{ n }+lambda, lambda in R , | vedclass

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

Question

$f(x)=2 x^{ n }+\lambda$

$f(4)=133$

$f(5)=255$

$133=2 	imes 4^{ n }+\lambda......(1)$

$255=2 	imes 5^{ n }+\lambda......(2)$

$(2) -(1

Vedclass · Accepted Answer

$60$

Vedclass · Answer

$f(x)=2 x^{ n }+\lambda$

$f(4)=133$

$f(5)=255$

$133=2 	imes 4^{ n }+\lambda......(1)$

$255=2 	imes 5^{ n }+\lambda......(2)$

$(2) -(1)$

$122=2\left(5^{ n }-4^{ n }ight)$

$\Rightarrow 5^{ n }-4^{ n }=61$

$	herefore n =3\, and\, \lambda=5$

Now, $f(3)-f(2)=2\left(3^3-2^3ight)=38$

Number of Divisors is $1,2,19,38$; and their sum is $60$.

Let $f ( x )=2 x ^{ n }+\lambda, \lambda \in R , n \in N$, and $f (4)=133$, $f(5)=255$. Then the sum of all the positive integer divisors of $( f (3)- f (2))$ is

Similar Questions

If $f(x) = \frac{{{x^2} - 1}}{{{x^2} + 1}}$, for every real numbers. then the minimum value of $f$

The domain of the derivative of the function $f(x) = \left\{ \begin{array}{l}{\tan ^{ - 1}}x\;\;\;\;\;,\;|x|\; \le 1\\\frac{1}{2}(|x|\; - 1)\;,\;|x|\; > 1\end{array} \right.$ is

Greatest value of the function, $f(x) = - 1 + \frac{2}{{{2^x}^2 + 1}}$ is

Set of all values of $x$ satisfying

$\frac{{{x^4} - 4{x^3} + 3{x^2}}}{{({x^2} - 4)({x^2} - 7x + 10)}} \ge 0$

The function $f(x) =$ ${x^{\frac{1}{{\ln \,x}}}}$