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    Operations with Functions

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    1. Solve: 7^3x-4=49

    2. Let f(x)=x^2+10x40
    -find vertex
    -state the range of the function
    -on what interval is the function increasing?

    3. Multiply and Simplify (7+6i)(2+9i)
    Write the answer in the form a+bi, where a and b are real numbers.

    © BrainMass Inc. brainmass.com December 24, 2021, 10:55 pm ad1c9bdddf
    https://brainmass.com/math/algebra/operations-functions-518729

    SOLUTION This solution is FREE courtesy of BrainMass!

    1. Solve: 7^3x-4=49

    Solution. As 49=7^2, 7^3x-4=49 <==> 7^3x-4=7^2.
    So, 3x-4=2
    i.e., 3x=6
    So, x=6/3=2

    2. Let f(x)=x^2+10x 40
    - find vertex
    - state the range of the function
    - on what interval is the function increasing?

    Solution: ******** I assume that f(x)=x^2+10x +40 *******

    We can rewrite f(x) as f(x)=(x+5)^2+15
    So,
    (1) the vertex of the parabola is (-5, 15);
    (2) As f(x)>=15, the range of f(x) is [15, infinity)
    (3) As the parabola is open upward, the function is increasing on [-5, infinity)

    3. Multiply and Simplify (7+6i)(2+9i)
    Write the answer in the form a+bi, where a and b are real numbers.

    Solution. Using the fact that i^2=-1, we have
    (7+6i)(2+9i) =7*(2+9i) +(6i)*(2+9i)
    =[14+63i]+ [12i - 54]
    =(14-54)+ (63+12)i
    = -40+75i.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 10:55 pm ad1c9bdddf>
    https://brainmass.com/math/algebra/operations-functions-518729

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