Anonymous
Anonymous asked in Science & MathematicsMathematics · 4 weeks ago

Need help in calculus reviewer?

Let f (x,y,z) = zxy + 2x. Use this definition of f to find the given functions.

Enter the fully simplified answer.

(a)

f(x+3y , x-3y , 2x^2)

 

= ???

(b)

f(4xy, 7y/x, 3xz)

= ???

TYIA ^^

1 Answer

Relevance
  • 4 weeks ago

    f(x, y, z) = zxy + 2x

    Just substitute and simplify:

    f(x + 3y, x - 3y, 2x²)

    Substitute the first into "x", second into "y", etc.:

    f(x, y, z) = zxy + 2x

    f(x + 3y, x - 3y, 2x²) = 2x²(x + 3y)(x - 3y) + 2(x + 3y)

    f(x + 3y, x - 3y, 2x²) = 2x²(x² - 3xy + 3xy - 9y²) + 2(x + 3y)

    f(x + 3y, x - 3y, 2x²) = 2x²(x² - 9y²) + 2(x + 3y)

    f(x + 3y, x - 3y, 2x²) = 2x⁴ - 18x²y² + 2x + 6y

    I'll leave the other one for you to work.

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