Maharashtra Board Solutions for Chapter: Functions, Exercise 2: EXERCISE

If $f\left(x\right)=2x^2+3, g\left(x\right)=5x-2$, then find $f\circ g$.

If $f\left(x\right)=4\left[x\right]-3$ where $\left[x\right]$ is greatest integer function of $x$, then find $f\left(-\frac{5}{2}\right)$.

If $f\left(x\right)=4\left[x\right]-3$, where $\left[x\right]$ is greatest integer function of $x$, then find $f\left(2\pi \right)$, where $\pi =3.14$.

If $f\left(x\right)=2\left\{x\right\}+5x$, where $\left\{x\right\}$ is fractional part function of $x$, then find $f(-1)$.

If $f\left(x\right)=2\left\{x\right\}+5x$, where $\left\{x\right\}$ is fractional part function of $x$, then find $f\left(\frac{1}{4}\right)$ (Write answer in decimal).

If $f\left(x\right)=2\left\{x\right\}+5x$, where $\left\{x\right\}$ is fractional part function of $x$, then find $f(-1.2)$.

If $f\left(x\right)=2\left\{x\right\}+5x$, where $\left\{x\right\}$ is fractional part function of $x$, then find $f(-6)$.

Solve for $x$: $2\left\{x\right\}=x+\left[x\right]$, where $\left[x\right]$ is greatest integer function and $\left\{x\right\}$ is a fractional part function.