We are provided with the following
[tex]{:\implies \quad \displaystyle \bf f(x) = \begin{cases} \bf 2x-3\quad for\:\: \bf x\geq 2 \\ \bf x\quad \bf for\:\: \bf x\< 2\end{cases}}[/tex]
And we need to find f(1) and then choose the choose the equivalent expression for f(1) from the given options . But , as two functions are defined by f(x) so let's define the function for x = 1
As f(x) = x , for x < 2 and 1 < 2 . So f(x) = x for x = 1 , now putting x as 1 ,so f(1) = 1
Now , also , as in all option their is f(2) , so let's find f(2) also , so that we can easily find the correct option , now as f(x) = 2x - 3 , for x ≥ 2 and 2 = 2 , so f(2) = 2(2) - 3 = 4 - 3 = 1
Now , As other options contains some constant multiplied by f(2) except option C) , so only f(2) will be 1 , and also f(1) = 1 , So f(1) = f(2)
Hence , Option C) f(2) is correct
