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Recent questions tagged functions

2 votes
0 answers
181
Function f and g
Let $f(x)$ mean that function $f$ ,applied to $x$,and $f^{n}(x)$ mean $f(f(........f(x)))$,that is $f$ applied to $x$ ,$n$ times.Let $g(x) = x+1$ and $h_{n}(x)=g^{n}(x).$Then what is $h_{9}^{8}(72)?$
Let $f(x)$ mean that function $f$ ,applied to $x$,and $f^{n}(x)$ mean $f(f(........f(x)))$,that is $f$ applied to $x$ ,$n$ times.Let $g(x) = x+1$ and $h_{n}(x)=g^{n}(x).$...
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1 votes
0 answers
189
ISI2016-MMA-21
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$? $\begin{pmatrix} 8 \\ 3 \end{pmatrix}$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 5^8$ $\begin{pmatrix} 8 \\ 3 \end{pmatrix} 8^5$ $\frac{8!}{3!}$
Let $A=\{1, 2, 3, 4, 5, 6, 7, 8 \}$. How many functions $f: A \rightarrow A$ can be defined such that $f(1)< f(2) < f(3)$?$\begin{pmatrix} 8 \\ 3 \end{pmatrix}$$\begin{pm...
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0 votes
0 answers
190
Why is composition of functions unequal in below question ?
Here Domain and co-Domain is Integers. I am getting fog=gof , what's wrong in this approach ?
Here Domain and co-Domain is Integers.I am getting fog=gof , what's wrong in this approach ?
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0 votes
0 answers
191
Injective Function
The number of ways possible to form injective function from set A set B where |A| = 3 and |B| = 5 such that pth element of set A cannot match with pthelement of set B are _________.
The number of ways possible to form injective function from set A set B where |A| = 3 and |B| = 5 such that pth element of set A cannot match with pthelement of set B are...
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1 votes
1 answer
195
MadeEasy Test Series: Calculus - Functions
Consider the following function $f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$ ... is defined on $R \rightarrow R-\{ \frac{1}{2} \}$, then it will be a bijection. Please let me know what's correct?
Consider the following function$f(x)=\frac{x}{2x+1} , \, x\not= -\frac{1}{2}$Is the function a bijection?Yes, this is a one-to-one function.For onto, let's suppose functi...
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0 votes
0 answers
196
#doubt
Let f∘gf∘g denote function composition such that (f∘g)(x)=f(g(x))(f∘g)(x)=f(g(x)). Let f:A→Bf:A→B such that for all g:B→Ag:B→A and h:B→Ah:B→A we have f∘g=f∘h⇒g=hf∘g=f∘h⇒g=h. Which of the following must be true? Ans: One-one. My doubt: WHY IT IS NOT ONTO ?
Let f∘gf∘g denote function composition such that (f∘g)(x)=f(g(x))(f∘g)(x)=f(g(x)). Let f:A→Bf:A→B such that for all g:B→Ag:B→A and h:B→Ah:B→A we have ...
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0 votes
1 answer
197
UGC NET CSE | July 2018 | Part 2 | Question: 87
Match the following in $\textbf{List-I}$ and $\textbf{List-II}$, for a function $f$ ... $\text{(a)-(ii), (b)-(i), (c)-(iii)}$ $\text{(a)-(ii), (b)-(iii), (c)-(i)}$
Match the following in $\textbf{List-I}$ and $\textbf{List-II}$, for a function $f$ :$\begin{array}{clcl} \text{} & \textbf{List-I} & & \textbf{List-II} \\ \text{(a)} & ...
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2 votes
2 answers
198
Recursion
int f (int n){ if (n==0) return 0; if(n==1) return 1; else return f(n-1)+f(n-2); } Find the upper bound and lower bound to the number of function calls for input size 'n'?
int f (int n){ if (n==0) return 0; if(n==1) return 1;elsereturn f(n-1)+f(n-2);}Find the upper bound and lower bound to the number of function ...
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4 votes
1 answer
201
Self Doubt. Related to https://gateoverflow.in/94634/gate1988-13ii#c216658.
1. If the set $S$ is countably infinite, prove or disprove that if $f$ maps $S$ onto $S$ (i.e $f:S \rightarrow S$ is a surjective function), then $f$ is one-to-one.
1. If the set $S$ is countably infinite, prove or disprove that if $f$ maps $S$ onto $S$ (i.e $f:S \rightarrow S$ is a surjective function), then $f$ is one-to-one.
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1 votes
1 answer
202
IIT M MS Question
Since given increasing,so $N'(t)>0$ but what will be $N''(t)$ for the slow rate part?
Since given increasing,so $N'(t)>0$ but what will be $N''(t)$ for the slow rate part?
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0 votes
0 answers
203
Domain of a function
What is the domain of the function log(log(sinx))?
What is the domain of the function log(log(sinx))?
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0 votes
1 answer
204
Function
Determine whether f is a function from the set of all bit strings to the set of integers if f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when S is the empty string ,the string with no bits.
Determine whether f is a function from the set of all bit strings to the set of integers if f(S) is the smallest integer i such that the ith bit of S is 1 and f(S)=0 when...
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3 votes
3 answers
207
ISRO2018-15
The domain of the function $\log (\log \sin(x))$ is: $0<x<$\pi$ $2n$\pi$<$x$<$(2n+1)$\pi$, for $n$ in $N$ Empty set None of the above
The domain of the function $\log (\log \sin(x))$ is:$0<x<$$\pi$$2n$$\pi$$<$$x$$<$$(2n+1)$$\pi$, for $n$ in $N$Empty setNone of the above
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0 votes
1 answer
208
PGEE 2018
Consider function f: N $\rightarrow$ N, where N is a natural number, which of the following function is not one to one but onto A) f(1)=f(2)=1 f(n)=n-1 B) 2n C) $n^{2}$
Consider function f: N $\rightarrow$ N, where N is a natural number, which of the following function is not one to one but ontoA) f(1)=f(2)=1 f(n)=n-1 B) 2nC) $n^{2}$
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