Let $R$ be the set of all real numbers. Let $f: R \rightarrow R$ be a function defined by $f(x) = \begin{cases} 2x-5 & x < -3 \\ x+2 & -3 \leq x < 5 \\ 3x+1 & x \geq 5 \end{cases}$
Match the following:
List-$I$
List-$II$
$(A) f(-5)+f(0)+f(-1)$
$(I) 16$
$(B) f(f(5)+10f(-3))$
$(II) 40$
$(C) f(f(-4))$
$(III) -31$
$(D) f(f(f(1)))$
$(IV) -12$
$(V) 19$
The correct match is:
Match the following:
| List-$I$ | List-$II$ |
| $(A) f(-5)+f(0)+f(-1)$ | $(I) 16$ |
| $(B) f(f(5)+10f(-3))$ | $(II) 40$ |
| $(C) f(f(-4))$ | $(III) -31$ |
| $(D) f(f(f(1)))$ | $(IV) -12$ |
| $(V) 19$ |
The correct match is:
- A$A-IV, B-V, C-III, D-I$
- B$A-V, B-IV, C-I, D-III$
- C$A-IV, B-V, C-II, D-I$
- D$A-IV, B-V, C-III, D-I$
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Similar Questions
Let $[t]$ be the greatest integer less than or equal to $t$. Let $A$ be the set of all prime factors of $2310$ and $f: A \rightarrow Z$ be the function $f(x) = \left[\log_2\left(x^2 + \left[\frac{x^3}{5}\right]\right)\right]$. The number of one-to-one functions from $A$ to the range of $f$ is:
DifficultJEE MAIN 2024
View SolutionMatch 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 |
$A$ function $f$ from the set of natural numbers $\mathbb{N}$ to the set of integers $\mathbb{Z}$ is defined by $f(n) = \begin{cases} \frac{n-1}{2}, & \text{if } n \text{ is odd} \\ -\frac{n}{2}, & \text{if } n \text{ is even} \end{cases}$. The function $f$ is:
The function $f(x) = x^{2} + bx + c$, where $b$ and $c$ are real constants, describes:
MediumWBJEE 2014
View SolutionThe set $A$ has $4$ elements and the set $B$ has $5$ elements. Then,the number of injective mappings that can be defined from $A$ to $B$ is:
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