Given
An equation that defines y as a function of x is given as,
[tex]3x-4y=1[/tex]To solve the equation for y in terms of x, and replace y with function notation f(x) and to find f(3).
Explanation:
It is given that,
[tex]3x-4y=1[/tex]That implies,
[tex]\begin{gathered} 3x-4y=1 \\ \Rightarrow4y=3x-1 \\ \Rightarrow y=\frac{3x-1}{4} \\ \Rightarrow y=\frac{3}{4}x-\frac{1}{4} \end{gathered}[/tex]Hence,
[tex]f(x)=\frac{3}{4}x-\frac{1}{4}[/tex]Also,
[tex]\begin{gathered} f(3)=\frac{3}{4}\times3-\frac{1}{4} \\ =\frac{9}{4}-\frac{1}{4} \\ =\frac{9-1}{4} \\ =\frac{8}{4} \\ =2 \end{gathered}[/tex]Hence, f(3)=2.
