For functions $f$ and $g$,where $f: [0, \frac{\pi}{2}] \rightarrow R$ with $f(x) = \sin x$ and $g: [0, \frac{\pi}{2}] \rightarrow R$ with $g(x) = \cos x$,which of the following is true?
- A$f+g$ is not one-one and $fg$ is not one-one
- B$f+g$ is not one-one and $fg$ is one-one
- C$f+g$ is one-one and $fg$ is one-one
- D$f+g$ is one-one and $fg$ is not one-one
Explore More
Similar Questions
The number of functions $f:[0,1] \rightarrow [0,1]$ satisfying $|f(x)-f(y)|=|x-y|$ for all $x, y \in [0,1]$ is
Let $f: R \rightarrow R$ be defined by $f(x) = \begin{cases} x + 2, & x \leq -1 \\ x^2, & -1 < x < 1 \\ 2 - x, & x \geq 1 \end{cases}$. Then the value of $f(-1.75) + f(0.5) + f(1.5)$ is
Let $f:[0,10] \rightarrow [1,20]$ be a function defined as $f(x) = \begin{cases} \frac{60-5x}{3}, & 0 \leq x \leq 6 \\ 10, & 6 \leq x \leq 7 \\ 31-3x, & 7 \leq x \leq 10 \end{cases}$. The function $f$ is:
Consider the function $f(x) = x^3 - 8x^2 + 20x - 13$. The function $f: R \rightarrow R$ is:
Match the functions of List-$I$ with their nature in List-$II$ and choose the correct option.
$A$. $f: R \rightarrow R$ defined by $f(x) = \cos(112x - 37)$ $I$. Injection but not surjection $B$. $f: A \rightarrow B$ defined by $f(x) = x|x|$ when $A = [-2, 2]$ and $B = [-4, 4]$ $II$. Surjection but not injection $C$. $f: R \rightarrow R$ defined by $f(x) = (x-2)(x-3)(x-5)$ $III$. Bijection $D$. $f: N \rightarrow N$ defined by $f(n) = n+1$ $IV$. Neither injection nor surjection $V$. Composite function
| $A$. $f: R \rightarrow R$ defined by $f(x) = \cos(112x - 37)$ | $I$. Injection but not surjection |
| $B$. $f: A \rightarrow B$ defined by $f(x) = x|x|$ when $A = [-2, 2]$ and $B = [-4, 4]$ | $II$. Surjection but not injection |
| $C$. $f: R \rightarrow R$ defined by $f(x) = (x-2)(x-3)(x-5)$ | $III$. Bijection |
| $D$. $f: N \rightarrow N$ defined by $f(n) = n+1$ | $IV$. Neither injection nor surjection |
| $V$. Composite function |
Vedclass Products
For Students
Vedclass Test Series
Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.
Start Free TrialFor Teachers
Exam Paper Generator
Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.
Try FreeFor Institutes
Online Exam Module
Live online exams with unlimited students, 360° analytics & white-label branding.
See Demo