Question

Cho f(x) = x^2-x-2

a,Tính \(f\left(\sqrt{a}\right),\sqrt{f\left(a\right)},f\left(a^2\right),\left[f\left(a\right)\right]^2\)

b,Tính giá trị nhỏ nhất của f(x)

Answer 1

a,\(f\left(\sqrt{a}\right)=\left(\sqrt{a}\right)^2-\sqrt{a}-2=a-\sqrt{a}-2\)

\(\sqrt{f\left(a\right)}=\sqrt{a^2-a-2}\)

\(f\left(a^2\right)=\left(a^2\right)^2-a^2-2=a^4-a^2-2\)

\(\left[f\left(a\right)\right]^2=\left(a^2-a-2\right)^2\)

b,\(f\left(x\right)=x^2-x-2=x^2-2\frac{1}{2}x+\frac{1}{4}-\frac{1}{4}-2\)

\(f\left(x\right)=\left(x-\frac{1}{2}\right)^2-\frac{9}{4}\)

Vì \(\left(x-\frac{1}{2}\right)^2\ge0\)

\(\Rightarrow GTNN\)của \(f\left(x\right)=\frac{-9}{4}\Leftrightarrow x=\frac{1}{2}\)