Functions and their graphs - class-XII
functions and their graphs
Questions
If f is even function and g is an odd function, then $f _og$ is ............function.
- Even
- Odd
- Neither even nor odd
- Either even
- True
- False
The identity function on real numbers given by $f(x)=x$ is continuous at every real numbers.
- True
- False
The minimum value of $f\left( x \right) ={ x }^{ 2 }+2x+3 ,x\in R$ is equal to
- $2$
- $3$
- $4$
- $1$
If $f:,\left( {3,6} \right) \to \left( {1,3} \right)$ is a function defined by $f\left( x \right) = x - \left[ {\frac{x}{3}} \right],,then,{f^{ - 1}}\left( x \right) = $
- $x-1$
- $x+1$
- $x$
- none of these
The tangents to the graph of the function $y=f(x)$ at the point with abscissa $x=1$ forms an angle of $\pi/6$ and the point $x=2$ an angle of $\pi/3$ and at the point $x=3$ an angle of $\pi/4$. The value of
$\displaystyle \int _{1}^{2}{f'(x)f''(x)dx}+\displaystyle \int _{2}^{3}{f''(x)dx}$
- $\dfrac{4\sqrt{3}-1}{3\sqrt{3}}$
- $\dfrac{3\sqrt{3}-1}{2}$
- $\dfrac{4-\sqrt{3}}{3}$
- $None\ of\ these$
The graph of the function $\cos x\cos x(x+2)-\cos^{2}(x+1)$ is
- A straight line through $(0, -\sin^{2}1)$ with slope $2$.
- A straight line through $(0, 0)$
- A parabola with vertex $(1, -\sin^{2}1)$
- A straight line through $\left(\dfrac{\pi}{2},-\sin^{2}1\right)$ and parallel to the $x-axis$.
If $f(x)=\left | \sin x \right |$, then domain of $f$ for the existence of inverse is
- $[0,\pi ]$
- $\left [ 0,\dfrac{\pi }{2} \right ]$
- $\left [ -\dfrac{\pi }{4},\dfrac{\pi }{4} \right ]$
- $\left [ -\dfrac{\pi }{2},\dfrac{\pi }{2} \right ]$