Answer:
• (a) x-10
,• (b) (1-10x)/x
Explanation:
Part A
Given the function:
[tex]y=1x+10[/tex]First, swap x and y:
[tex]x=1y+10[/tex]Next, make y the subject of the equation:
[tex]y=x-10[/tex]Therefore:
[tex]f^{-1}(x)=x-10[/tex]Part B
Given the function:
[tex]y=\frac{1}{x+10}[/tex]First, swap x and y:
[tex]x=\frac{1}{y+10}[/tex]Next, make y the subject of the equation:
[tex]\begin{gathered} x=\frac{1}{y+10} \\ x(y+10)=1 \\ y+10=\frac{1}{x} \\ y=\frac{1}{x}-10 \\ y=\frac{1-10x}{x} \end{gathered}[/tex]Therefore:
[tex]f^{-1}(x)=\frac{1-10x}{x}[/tex]