Question

A function $f:[1,6)\to R$ is defined as follows :
$f\left(x\right)=$ $\{\begin{array}{c}1+x,1\le x<2\\ 2x-1,2\le x<4\\ 3x^2-10,4\le x<6\end{array}$ (Here, $[1,6)=\{x\in R:1\le x<6\}$)
Find the values of
a) $f\left(5\right)$
b) $f\left(3\right)$
c) $f\left(1\right)$
d) $f\left(2\right)-f\left(4\right)$
e) $2f\left(5\right)-3f\left(1\right)$

Answer 1

Given, $f\left(x\right)=$ $\{\begin{array}{c}1+x,1\le x<2\\ 2x-1,2\le x<4\\ 3x^2-10,4\le x<6\end{array}$
a) $f\left(5\right)=3{\left(5\right)}^2-10$
$=3\left(25\right)-10$
$=75-10=65$
b) $f\left(3\right)=2\left(3\right)-1=6-1=5$
c) $f\left(1\right)=1+1=2$
d) $f\left(2\right)=2\left(2\right)-1=4-1=3$
$f\left(4\right)=3{\left(4\right)}^2-10=3\left(16\right)-10=48-10=38$
$f\left(2\right)-f\left(4\right)=3-38=-35$
e) $2f\left(5\right)-3f\left(1\right)=2\left(65\right)-3\left(2\right)$
$=130-6=124$