1 Answer

Gangesh · Answer 1 · 2023-10-17T13:46:30+0000

${ \qquad\qquad\huge\underline{{\sf Answer}}}$

Here we go ~

In the above question, it is given that :

$\qquad \sf  \boxed{ \sf f(x) = (x + 3)/(2) }$

A.) Find f(2) :

$\qquad \sf  \dashrightarrow \: f(2) = (2 + 3)/(2)$

$\qquad \sf  \dashrightarrow \: f(2) = (5)/(2)$

or

$\qquad \sf  \dashrightarrow \: f(2) = 0.5$

B.) Find
${ \sf {f}^(-1)(x) }$ :

$\qquad \sf  \dashrightarrow \: let \: y = f (x)$

so, we can write it as :

$\qquad \sf  \dashrightarrow \: y = (x + 3)/(2)$

$\qquad \sf  \dashrightarrow \: 2y = x + 3$

$\qquad \sf  \dashrightarrow \: x = 2y - 3$

Now, put x =
${ \sf {f}^(-1)(x) }$ , and y = x and we will get our required inverse function ~

$\qquad \sf  \dashrightarrow \: f {}^( - 1)(x) = 2x- 3$

C.) Find
${ \sf {f}^(-1)(12) }$ :

$\qquad \sf  \dashrightarrow \: f {}^( - 1)(12) = 2(12)- 3$

$\qquad \sf  \dashrightarrow \: f {}^( - 1)(12) = 36- 3$

$\qquad \sf  \dashrightarrow \: f {}^( - 1)(12) = 33$

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