Question

f is a function defined by
$\large\boxed{\sf{ \int (x) = \binom{2x + 4 \: \: \: \: \: \: \: \: x \leqslant 2}{2x - 1 \: \: \: \: \: \: \: \: x > 2} }}$
Find f(0), f(2) and f(4).​

Answer 1

Appropriate Question :-

If f is a function defined by

$\begin{gathered}\begin{gathered}\bf\: f(x) = \begin{cases} &\sf{2x + 4 \: \: \: \: \: when \: x \leqslant 2} \\ \\ &\sf{2x - 1 \: \: \: \: \: when \: x > 2} \end{cases}\end{gathered}\end{gathered}$

Find f(0), f,(2) and f(4).

$\large\underline{\sf{Solution-}}$

Given function is

$\begin{gathered}\begin{gathered}\bf\: f(x) = \begin{cases} &\sf{2x + 4 \: \: \: \: \: when \: x \leqslant 2} \\ \\ &\sf{2x - 1 \: \: \: \: \: when \: x > 2} \end{cases}\end{gathered}\end{gathered}$

Calculation of f(0)

Given that,

$\rm \: f(x) = 2x + 4 \: \: \: \: when \: x \leqslant 2$

So,

$\rm \: f(0)$

$\rm \: = \: 2 \times 0 + 4$

$\rm \: = \: 0 + 4$

$\rm \: = \: 4$

So,

$\rm\implies \:\boxed{ \rm{ \:f(0) = 4 \: \: }}$

Calculation of f(2)

Given that

$\rm \: f(x) = 2x + 4 \: \: \: \: when \: x \leqslant 2$

So,

$\rm \: f(2)$

$\rm \: = \: 2 \times 2 + 4$

$\rm \: = \: 4 + 4$

$\rm \: = \: 8$

Hence,

$\rm\implies \:\boxed{ \rm{ \:f(2) = 8 \: \: }}$

Calculation of f(4)

Given that,

$\rm \: f(x) = 2x - 1 \: \: \: \: \: when \: x > 2$

So,

$\rm \: f(4)$

$\rm \: = \: 2 \times 4 - 1$

$\rm \: = \: 8 - 1$

$\rm \: = \: 7$

Hence,

$\rm\implies \:\boxed{ \rm{ \:f(4) = 7 \: \: }}$