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If f : `B to N , g : N to N and h : N to R ` defined as f(x) = 2x , g(y) = `3y+4` and h(x) = sin x , `AA` x, y, z in N . Show that h ` h o ( g of) = (h og) o f `

Answer

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Consider f: N to N, g : N to N and h: N to R defined as f(x) = 2x, g(y) = 3y + 4 and h(z) = sin z, AA x, y and z in N. Show that ho(gof) = (hog)of .

Consider f:N to N, g : N to N and h: N to R defined as f (x) =2x,g (h) = 3y + 4 and h (z= sin z, AA x, y and z in N. Show that h(gof) = (hog) of.

Knowledge Check

  • Let f, g : R rarrR be two functions defined as f(x) = |x| + x and g(x) = | x| - x AA x in R. . Then (fog ) (x) for x lt 0 is

    A
    0
    B
    4x
    C
    `-4x`
    D
    2x

  • If f(x) = x^n , n in N and gof(x) = ng(x) , then g(x) can be

    A
    `n|x|`
    B
    `3x^1/3`
    C
    `e^x`
    D
    `log|x|`

  • If f: R rarr R be defined by , f(x) = 10x - 7 and g = f^-1 , then g(x)

    A
    `1//10x - 7`
    B
    `1//10x +7`
    C
    `x+7//10'
    D
    `x-7//10`

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    Let fg: R to R be defined respectively by f(x) = x+1, g(x) = 2x-3 . Find f+g, f-g and f/g .

    If f:R rarr R and g : R rarr R are defined by f(x) = 3x + 2 and g(x) = x^2 - 3 , then the value of x such that g(f(x))=4 are

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