Question

f:x=4x+m and f^-1:x=nx+3/4. Find the values of m and n. @ganeshie8

Answer 1

f:x means function of x?

Answer 2

is the answer -3 and 1/4

Answer 3

yes

Answer 4

find the inverse of
\(f(x)=4x+m\)

Answer 5

y=4x+m

Answer 6

\[\frac{ y-m }{ 4 }=x\]

Answer 7

\[f ^{-1}(x)=\frac{ x-m }{ 4 }\]

Answer 8

ok compare the two inverse equations now

Answer 9

\(\large \begin{align} \color{black}{nx+\dfrac{3}{4}=\dfrac{x-m}{4} \hspace{.33em}\\~\\
\implies nx+\dfrac{3}{4}=x\cdot\dfrac{1}{4}+\dfrac{-m}{4} \hspace{.33em}\\~\\
}\end{align}\)

Answer 10

\[\frac{ 3 }{ 4 }=\frac{ -m }{ 4 }\]

Answer 11

\[-4m=12\]

Answer 12

\[m=-3\]

Answer 13

\(\large \begin{align} \color{black}{nx+\dfrac{3}{4}=\dfrac{x-m}{4} \hspace{.33em}\\~\\
\implies \color{red}{n}x+\color{blue}{\dfrac{3}{4}}=x\cdot\color{red}{\dfrac{1}{4}}+\color{blue}{\dfrac{-m}{4}} \hspace{.33em}\\~\\
}\end{align}\)

Answer 14

Thnx @mathmath333 :)

Answer 15

yw