Find the maximum value of f(x) = sin(sinx) for all x ∈ R

Question

Find the maximum value of f(x) = sin(sinx) for all x ∈ R (A) -sin 1 (B) sin 6 (C) sin 1 (D) -sin 3

Tardigrade Admin · Accepted Answer

We have f(x) = sin (sin x), x ∈ R Now, -1 le sin x le 1 for all x ∈ R ⇒ sin (-1) le sin(sinx) le sin 1 for all x ∈ R [∵ sin x is an increasing function on [-1,1 ]] ⇒ - sin 1 le f(x) le sin 1 for all x ∈ R This shows that the maximum value of f(x) is sin 1.

Q. Find the maximum value of $f (x) = s in (s in x)$ for all $x \in R$

$- s in 1$

$s in 6$

$s in 1$

$- s in 3$

Q. Find the maximum value of f(x)=sin(sinx) for all x∈R

−sin1

sin6

sin1

−sin3

We have f(x)=sin(sinx), x∈R Now, −1≤sinx≤1 for all x∈R ⇒sin(−1)≤sin(sinx)≤sin1 for all x∈R [∵sinx is an increasing function on [−1,1]] ⇒−sin1≤f(x)≤sin1 for all x∈R This shows that the maximum value of f(x) is sin1.

Q. Find the maximum value of $f (x) = s in (s in x)$ for all $x \in R$

$- s in 1$

$s in 6$

$s in 1$

$- s in 3$