algebra

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use f(x)=square root of 5-x and g(x)=x^2 + 2x
a-find f(g(x)), state the domain
b-find g(f(x)),state the domain
c-find g(f(-1))
d-find f(x)/g(x), state the domain, then evaluate for x=3

  • algebra -

    f(x) = √(5-x) , g(x) = x^2 + 2x

    f(g(x)
    = √(5 - (x^2+2x) )
    = √(5 - x^2 - 2x)

    for this to be real, 5 - x^2 - 2x ≥ 0
    x^2 + 2x - 5 ≤ 0
    solve x^2 + 2x - 5 = 0 ,
    the domain will be all values of x between the two solution values

    g(f(x)
    = (√(5-x))^2 + 2√(5-x)
    = 5 - x + 2√(5-x)
    domain is :
    5-x ≥ 0
    -x ≥ -5
    x ≤ 5

    you try c and d

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