Calculus homework help?

Let f (x,y,z) = 4zxy + 5x. Use this definition of f to find the given functions.

Enter the fully simplified answer.

(a)

f(x+2y,x-2y,4x^2)

= ???

(b)

f(7xy,9y/x,9xz)

= ???

TYIA ^^

1 Answer

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  • TomV
    Lv 7
    4 weeks ago

     f (x,y,z) = 4zxy + 5x

    Remember, the "x, y, and z" in the function definition are nothing but placeholders for the values specified in the (x,y,z) positions in the function argument.

    a) f(x+2y,x-2y,4x^2)

    Replace x, y, and z in the function definition with x+2y, x-2y, and 4x² respectively

    = 4(4x²)(x+2y)(x-2y) + 5(x+2y)

    = 16x²(x² - 4y²) + 5x + 10y

    = 16x⁴ - 64x²y² + 5x + 10y

    b) f(7xy,9y/x,9xz)

    Replace x, y, and z in the function definition with 7xy, 9y/x, and 9xz respectively

    = 4(9xz)(7xy)(9y/x) + 5(7xy)

    = 2268xy²z + 35xy

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