Given:
[tex]f(x)=\frac{1}{4x+10}[/tex]
Required:
To find the inverse of a givne function.
Explanation:
Consider the given function
[tex]f(x)=\frac{1}{4x+10}[/tex][tex]y=\frac{1}{4x+10}[/tex]
Swap x and y, we get
[tex]x=\frac{1}{4y+10}[/tex]
Now solve for y.
[tex]\begin{gathered} 4y+10=\frac{1}{x} \\ \\ 4y=\frac{1}{x}-10 \\ \\ y=\frac{1}{4x}-\frac{10}{4} \\ \\ y=\frac{1}{4x}-\frac{5}{2} \end{gathered}[/tex]
Now
[tex]\begin{gathered} f^{-1}(x)=\frac{1}{4x}-\frac{5}{2} \\ \\ =\frac{1-10x}{4x} \end{gathered}[/tex]
Final Answer:
[tex]f^{-1}(x)=\frac{1}{4x}-\frac{5}{2}[/tex]
