Exercise 1.1.33

Question

If $f(x) = 3x^2-x+ 2$, find $f(2), f(-2), f(a), f(-a), f (a+ 1), 2f(a), f (2a), f(a^2), [f(a)]^2,$ and $f(a +h)$.

Khagan Gulusoy · Accepted Answer

$$f(2)=3\cdot 2^2-2+2=12;$$
$$f(-2)=3\cdot 4+2+2=16;$$
$$f(a)=3a^2-a+2;$$
$$f(-a)=3\cdot (-a)^2-(-a)+2=3\cdot a^2+a+2;$$
$$f(a+1)=3(a+1)^2-(a+1)+2=3(a^2+2a+1)-a-1+2=3a^2+6a+3-a+1=3a^2+5a+4;$$
$$2f(a)=2(3a^2-a+2)=6a^2-2a+4;$$
$$f(2a)=3\cdot (2a)^2-2a+2=3\cdot 4a^2-2a+2=12a^2-2a+2;$$
$$f(a^2)=3(a^2)^2-a^2+2=3a^4-a^2+2;$$
$$(f(a))^2= (3a^2-a+2)^2=9 a^4 - 6 a^3 + 13 a^2 - 4 a + 4;$$
$$f(a+h)=3(a+h)^2-a-h+2=3(a^2+2ah+h^2)-a-h+2=3a^2+6ah+3h^2-a-h+2.$$

Exercise 1.1.33

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Exercise 1.1.33

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