suatu fungsi linear f memiliki nilai 5 saat x = 4 dan nilai -7 saat x = -2. maka tentukanlah rumus d.... Question from @SasukeUchiha01

October 2022 1 38 Report

suatu fungsi linear f memiliki nilai 5 saat x = 4 dan nilai -7 saat x = -2. maka tentukanlah rumus dari fungsi tersebut
------------------
[tex] \\ \\ [/tex]

3A01

$\mathbb{ \color{aqua}{ \underbrace{JAWABAN}}}$

$\boxed{ \bf{ \: f(x) = 2x - 3} \: }$

------------------

$\mathbb{ \color{orange}{ \underbrace{PENYELESAIAN}}}$

$\boxed{ \: \begin{aligned} \tt{f(4)} &= \tt{a(4) + b = 5} \\ &= \tt{ \pink{4a + b = 5}.......(1)} \\ \tt{f( - 2)} &= \tt{a( - 2) + b = - 7} \\ &= \tt{ \pink{ - 2a + b = - 7}....(2)} \end{aligned} \: } \\ \\$

eliminasi : b

$\boxed{ \: \begin{aligned} \tt{4a + \not{b}} &= \tt{5} \\ \tt{ - 2a + \not{b}} &= \tt{ - 7} \\ \underline{~~~~~~~~~~~~~~~} & \underline{~~~~~~~~~~~~} - \\ \tt{6a} &= \tt{12} \\ \tt{a} &= \tt{ \frac{12}{6} } \\ \tt{a} &= \tt{ \pink{2}} \end{aligned} \: } \\ \\$

substitusikan a = 2 ke salah satu persamaan

$\boxed{ \: \begin{aligned} \tt{4a + b} &= \tt{5} \\ \tt{4(2) + b} &= \tt{5} \\ \tt{8 + b} &= \tt{5} \\ \tt{b} &= \tt{5 - 8} \\ \tt{b} &= \tt{ \pink{ - 3}} \end{aligned} \: } \\ \\$

rumus fungsi

$\boxed{ \: \begin{aligned} \tt{f(x)} &= \tt{ax + b} \\ \tt{f(x)} &= \tt{2x + ( - 3)} \\ \pink{ \bf{f(x})} & \pink{= \bf{2x - 3}} \end{aligned} \: }$

------------------

$\mathbb{ \color{magenta}{ \underbrace{PEMBUKTIAN}}}$

substitusikan x = 4 dan x = -2

$\boxed{ \: \begin{array}{c|c} \begin{aligned} \tt{f(x)} &= \tt{2x - 3} \\ \tt{f(4)} &= \tt{2(4) - 3} \\ \tt{f(4)} &= \tt{8 - 3} \\ \tt{f(4)} &= \tt{ \pink{5}} \end{aligned} & \begin{aligned} \tt{f(x)} &= \tt{2x - 3} \\ \tt{f( - 2)} &= \tt{2( - 2) - 3} \\ \tt{f( - 2)} &= \tt{ - 4 - 3} \\ \tt{f( - 2)} &= \tt{ \pink{ - 7}} \end{aligned} \end{array} \: }$

------------------

$\mathbb{ \color{red}{ \underbrace{KESIMPULAN}}}$

Jadi, rumus dari fungsi tersebut adalah f(x) = 2x - 3

$\colorbox{ff0000}{} \colorbox{ff4000}{}\colorbox{ff8000}{}\colorbox{ffc000}{}\colorbox{ffff00}{}\colorbox{c0ff00}{}\colorbox{80ff00}{}\colorbox{40ff00}{}\colorbox{00ff00}{}\colorbox{00ff40}{}\colorbox{00ff80}{}\colorbox{00ffc0}{}\colorbox{00ffff}{}\colorbox{00c0ff}{}\colorbox{0080ff}{}\colorbox{0040ff}{}\colorbox{0000ff}{}\colorbox{4000ff}{}\colorbox{8000ff}{}\colorbox{c000ff}{}\colorbox{ff00ff}{}\colorbox{ff00c0}{}\colorbox{ff00a0}{}\colorbox{ff0080}{}\colorbox{ff0040}{}$