Question

An equation that defines y as a function of x is given.3x-4y=1(a) Solve the equation for y in terms of x, and replace y with function notation f(x).F(x)= ______Find f(3) F(3)=_______(Type an integer or simplified fraction)

Answer 1

Given

An equation that defines y as a function of x is given as,

`3x-4y=1`

To solve the equation for y in terms of x, and replace y with function notation f(x) and to find f(3).

Step-by-step explanation:

It is given that,

`3x-4y=1`

That implies,

`\begin{gathered} 3x-4y=1 \\ \Rightarrow4y=3x-1 \\ \Rightarrow y=(3x-1)/(4) \\ \Rightarrow y=(3)/(4)x-(1)/(4) \end{gathered}`

Hence,

`f(x)=(3)/(4)x-(1)/(4)`

Also,

`\begin{gathered} f(3)=(3)/(4)*3-(1)/(4) \\ =(9)/(4)-(1)/(4) \\ =(9-1)/(4) \\ =(8)/(4) \\ =2 \end{gathered}`

Hence, f(3)=2.