Jawab dengan menggunakan Cara....... Question from @johanasoegiartpd1daj

JavierSKho13

Penjelasan dengan langkah-langkah:

FUNGSI INVERS

• f(x) = 4x – 11

misal f(x) = p

maka,

p = 4x – 11

4x = p + 11

x = p + 11

→ f-¹(x) = ¼(p + 11) ✔

f-¹(5) = ¼(5 + 11)

f-¹(5) = ¼(16)

f-¹(5) = 16

→ f-¹(5) = 4 ✔✔

• h(x) = x + 7

3x – 5

umpama h(x) = R

R = x + 7

3x – 5

R(3x – 5) = x + 7

3Rx – 5R = x + 7

3Rx – x = 5R + 7

x(3R – 1) = 5R + 7

x = 5R + 7

3R – 1

→ h-¹(x) = 5x + 7 ✔

3x – 1

1 votes Thanks 1

JΟY

Diketahui ${\sf{f(x)=4x-11}}$ . Invers fungsi ${\sf{f}}$ dari ${\sf{f^{-1}(5)}}$ adalah ${\sf{4}}$

Diketahui ${\sf{h(x)=\dfrac{x+7}{3x-5},\ne\dfrac{5}{3}}}$ . Invers fungsi ${\sf{h}}$ dari ${\sf{h^{-1}(x)}}$ adalah ${\sf{\dfrac{5x+7}{3x-1}}}$

Penjelasan dengan langkah-langkah :

Misal : h(x) = y

Maka :

$\begin{aligned}{\sf{f(x)}}&={\sf{4x-11}}\\{\sf{y}}&={\sf{4x-11}}\\{\sf{4x}}&={\sf{-11+y}}\\{\sf{4x}}&={\sf{y+11}}\\{\sf{x}}&={\sf{\frac{y+11}{4}}}\\{\sf{f^{-1}(x)}}&={\sf{\frac{x+11}{4}}}\\{\sf{f^{-1}(5)}}&={\sf{\frac{5+11}{4}_{\dots(substitusi~x=5)}}}\\{\sf{f^{-1}(5)}}&={\sf{\frac{16}{4}}}\\{\sf{f^{-1}(5)}}&={\sf{4}}\\\end{aligned}$

–––

Misal : h(x) = y

Maka :

$\begin{aligned}{\sf{h(x)}}&={\sf{\frac{x+7}{3x-5}}}\\{\sf{y}}&={\sf{\frac{x+7}{3x-5}}}\\{\sf{y(3x-5)}}&={\sf{x+7}}\\{\sf{3xy-5y}}&={\sf{x+7}}\\{\sf{3xy-x}}&={\sf{5y+7}}\\{\sf{x(3y-1)}}&={\sf{5y+7}}\\{\sf{x}}&={\sf{\frac{5y+7}{3y-1}}}\\{\sf{f^{-1}(x)}}&={\sf{\frac{5x+7}{3x-1}}}\end{aligned}$

2 votes Thanks 9

FUNGSI INVERS

→ f-¹(x) = ¼(p + 11) ✔

→ f-¹(5) = 4 ✔✔

→ h-¹(x) = 5x + 7 ✔

3x – 1

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