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Functions Test ...

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  • Question 1
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    Consider the following functions are odd function in their default domains
    (i) $$\cfrac { { 2 }^{ x }-1 }{ { 2 }^{ x }+1 } $$
    (ii) $$\cfrac { { x }^{ 2 }+1 }{ x\sin { x }  } $$
    (iii) $$\ln { \left( \cfrac { 1+x }{ 1-x }  \right)  } $$
    (iv) $$x{ e }^{ \left| x \right| +\cos { x }  }\quad $$
    Which of these is/are odd

  • Question 2
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    Let $$A = \{ 1,2,3,4,5,6\} .$$ The number of onto functions from $$A$$ to$$A$$ such that.$$f\left( x \right) \ne x$$ for all $$x \in A$$ is

  • Question 3
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    Let $$f:A \to b$$ be a function defined by f(x) =$$\sqrt {1 - {x^2}} $$

  • Question 4
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    Let $$f$$, $$g:R\rightarrow {R}$$ be two functions defined as $$ f\left( x \right) =\left| x \right| +x$$, $$ g\left( x \right) =\left| x \right| -x, \forall x\in R$$. Then, find $$fog(x)$$ 

  • Question 5
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    Consider set $$A={1,2,3,4}$$ and set $$B={0,2,4,6,8}$$, then the number of one-one function from set $$A$$ to set $$B$$ is ?

  • Question 6
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    If $$g\left( x \right) = {x^2} + x - 2$$ and $$\frac{1}{2}gof\left( x \right) = 2{x^2} + 5x + 2$$, then $$f\left( x \right)$$ is

  • Question 7
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    Let f : $$R \to R$$ and g : $$R \to R$$ be two one-one and onto functions such that they are the mirror images of each other about the line y = 2. If h(x) = f(x) + g(x), then h(0) equal to

  • Question 8
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    If $$f(x)=2x+5$$ and $$g(x)=x^2+1$$ be two real function , then value of $$fog$$ at x=1

  • Question 9
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    $$c \to c\,\,is\,defined\,as\,f\left( x \right) = \frac{{ax + b}}{{cx + d}}\,\,bd \ne 0$$.then f is a constant function when

  • Question 10
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    Let $$A$$ be a set of $$4$$ elements and $$B$$ has $$3$$ elements . From the set of all functions from $$A$$ to $$B$$, the probability that it is an onto function is

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