Find the range of the following functions y = x + √ x + 1 f (x) = (x + 5) / (X & # 178; + 4) Don't be wrong

Find the range of the following functions y = x + √ x + 1 f (x) = (x + 5) / (X & # 178; + 4) Don't be wrong

(1) Let √ x + 1 = t (t ≥ 0)
x=t^2-1
y=t^2-1+t=(t+1/2)^2-5/4
Because t ≥ 0
Properties of quadratic function
Y increases monotonically when t ≥ 0
So the minimum value is (- 1) ^ 2-1-1 = - 1
That is, the value range is [- 1, + OO)
(2)y=(x+5)/(x^2+4)
yx^2+4y=x+5
yx^2-x+4y-5=0
Want x to exist
That is △≥ 0
1-4y(4y-5)≥0
1-16y^2+20y≥0
16y^2-20y-1≤0
（5-√29)/8≤y≤(5+√29)/8
So the range is [(5 - √ 29) / 8, (5 + √ 29) / 8]