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March 30, 2017

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Okay so I need help with basically how to find the domain, range, and how to solve if it says Find the value of f(3).

Let the f function be defined by f(x) = the square root of x + 1 for -1 is less than or equal to x less than or equal to 3.
And 4 - x for 3 is less than x less than or equal to 5

I don't know where to start. Thanks in advance.

  • Algebra 2 - ,

    we have:

    f(x) =
    {√(x+1) for -1 <= x <= 3
    {4-x for 3 < x <= 5

    domain:
    square root is only defined for positive values. So, we need x+1 >= 0, or x >= -1. 4-x is defined for all real x.
    So, domain is [-1,5]

    range:
    for -1 <= x <= 3, 0 <= f(x) <= 2
    for 3 < x <= 5, -1 <= f(x) < 1
    so, the range is [-1,2]

    f(3) = √(3+1) = √4 = 2

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