Answer:
The function values of [tex]{q(2)}[/tex] is [tex]\bold{\dfrac{11}{4}}[/tex], [tex]q(0)[/tex] is UNDEFINED and [tex]q(-x)[/tex] is [tex]\bold{2+\dfrac{3}{x^2}}[/tex]
Step-by-step explanation:
Given,
[tex]q(t)=\dfrac{2t^2+3}{t^2}[/tex]
Part (a)
Find [tex]q(2)[/tex]
Put [tex]2[/tex] for [tex]t[/tex] for finding the value of the function [tex]q(2)[/tex].
Therefore,
[tex]\begin{aligned}q(2)&=\dfrac{2\times2^2+3}{2^2}\\&=\dfrac{8+3}{4}\\&=\dfrac{11}{4}\end{aligned}[/tex]
Part (b)
Find [tex]q(0)[/tex]
Put [tex]0[/tex] for [tex]t[/tex] for finding the value of the function [tex]q(0)[/tex].
[tex]\begin{aligned}q(0)&=\dfrac{2\times0^2+3}{0^2}\\&=\dfrac{3}{0}\\&=\infty\end{aligned}[/tex]
Part (c)
Find [tex]q(-x)[/tex]
Put [tex]-x[/tex] for [tex]t[/tex] for finding the value of the function [tex]q(-x)[/tex].
Therefore,
[tex]\begin{aligned}q(-x)&=\dfrac{2\times(-x)^2+3}{(-x)^2}\\&=\dfrac{2x^2+3}{x^2}\\&=2+\dfrac{3}{x^2}\end{aligned}[/tex]
