Question

已知函数 ( p(x) = x^2 + 4 )，( q(x) = sqrt{x + 5} )，分别计算：((q cdot p)(4) = square)，((p cdot q)(4) = square)（下方有操作按钮和计算框）

Explanation:

Step1: Define $(q-p)(x)$

$(q-p)(x) = q(x) - p(x)$

Step2: Substitute given functions

$(q-p)(x) = \sqrt{x+1} - (x^2 + 4)$

Step3: Evaluate at $x=4$

First calculate $p(4) = 4^2 + 4 = 16 + 4 = 20$
Then calculate $q(4) = \sqrt{4+1} = \sqrt{5}$
So $(q-p)(4) = \sqrt{5} - 20$

Step4: Define $(p-q)(x)$

$(p-q)(x) = p(x) - q(x)$

Step5: Evaluate at $x=4$

$(p-q)(4) = p(4) - q(4) = 20 - \sqrt{5}$

Answer:

$(q-p)(4) = \sqrt{5} - 20$
$(p-q)(4) = 20 - \sqrt{5}$