Question

let f and g be defined by the table to the right. find the following.
\\(\sqrt{f(-1)-f(0)}-g(2)^{2}+f(-2)+g(2)\cdot g(-1)\\)
\\(\sqrt{f(-1)-f(0)}-g(2)^{2}+f(-2)+g(2)\cdot g(-1)=\square\\) (simplify your answer.)

Explanation:

Step1: Find f(-1), f(0), g(2), f(-2), g(-1) from the table

From the table, f(-1) = 4, f(0)= - 5, g(2)= - 5, f(-2)=5, g(-1)=8

Step2: Calculate \(\sqrt{f(-1)-f(0)}\)

Substitute f(-1) = 4 and f(0)= - 5 into \(\sqrt{f(-1)-f(0)}\), we get \(\sqrt{4-(-5)}=\sqrt{4 + 5}=\sqrt{9}=3\)

Step3: Calculate \([g(2)]^{2}\)

Substitute g(2)= - 5 into \([g(2)]^{2}\), we get \((-5)^{2}=25\)

Step4: Calculate \(g(2)\cdot g(-1)\)

Substitute g(2)= - 5 and g(-1)=8 into \(g(2)\cdot g(-1)\), we get \((-5)\times8=-40\)

Step5: Calculate the whole expression

\(\sqrt{f(-1)-f(0)}-[g(2)]^{2}+f(-2)+g(2)\cdot g(-1)=3 - 25+5+( - 40)\)
\(=3+5-25 - 40=8-65=-57\)

Answer:

-57