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Functions

A test by Gaurav Jain.

Test Questions
  1. Question

    Find f(4) if f(x)=x^4-3x^3+6x^2-10x+16

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  2. Question

    If f(x)=2x \quad and \quad g(x)=x+1 . Find (gof)(x)

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  3. Question

    If f(x, y)=3x^2-2xy-y^2+4 . Find (1,-1)

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  4. Question

    If f(x)=3x-5 \quad and \quad f[g(x)]=2x . Find g(x)

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  5. Question

    If f(x)=ax^2+bx+2.f(1)=3 \quad and \quad f(4)=42 . Find 'b'

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  6. Question

    The functions f and g are defined for natural numbers as:
    F(x)=1+x^2 , if x is even
    =(1+x)^2, otherwise
    G(x)=(x-1)^2 , if x is prime
    =x^2-1 , otherwise
    For which number is F[G(x)]=\{1+[(x-1)^2]^2\} .

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  7. Question

    The functions f and g are defined for natural numbers as:
    F(x)=1+x^2 , if x is even
    =(1+x)^2, otherwise
    G(x)=(x-1)^2 , if x is prime
    =x^2-1 , otherwise
    Find if F(2)+g(1)=F(2) .

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  8. Question

    The functions f and g are defined for natural numbers as:
    F(x)=1+x^2 , if x is even
    =(1+x)^2, otherwise
    G(x)=(x-1)^2 , if x is prime
    =x^2-1 , otherwise
    Find if F(5)=G(7) .

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  9. Question

    The functions f and g are defined for natural numbers as:
    F(x)=1+x^2 , if x is even
    =(1+x)^2, otherwise
    G(x)=(x-1)^2 , if x is prime
    =x^2-1 , otherwise
    Find if G(3)/F(3)=4 .

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  10. Question

    If f(x)=2x^2-4 is f(x) even or odd function?

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