Convexity

Q. The fundamental period of the function $f\left(x\right)=3+2\sin \left\{\frac{(\pi x+2)}{3}\right\}$ is

Q. Let $f\left(x\right)=x^2,g\left(x\right)=2^x$. The number of integers in the solution set of $fog\left(x\right)=gof\left(x\right)$ is

1. $1$
2. $0$
3. $2$
4. $3$

Q.

If a function f(x) is convex at x = a, then f”(a) < 0.

1. True

2. False

Q.

Find the interval(s) in which f(x) = sec(x) is convex.

1. $(-\pi /2,\pi /2)$

2. $(\pi /2,3\pi /2)$

3. $(3\pi /2,5\pi /2)$

4. $(5\pi /2,7\pi /2)$