- Let
*f(*sin(cos*x*) =*x*), then check whether it is increasing or decreasing in - Show that
*x*^{3}– 3*x*^{2}– 9*x*+ 20 is positive for all values of*x*> 4. - Solve for
*x*: (*x*+ 3)^{5}– (*x*– 1)^{5}≥ 244 - Find range of
a. *x*^{x}b. log[(sin *x*)^{sin x}+ 1] - Show that
*e*^{x – 1}+*x*= 2 has only one real root.

**1.** Decreasing

**3.** [0, ∞)

**4.** (a) [*e*^{–1/e}, ∞)

(b) [log(*e*^{–1/e} + 1), log 2]

- If
*f*: ℝ → ℝ is decreasing and*g*: ℝ → ℝ is increasing then which of the following functions is increasinga. *f o f*b. *g o g*c. *f o g*d. *g o f* - The function is increasing function of
*x*ifa. *ab > cd*b. *ad > ...*

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