Answer:
for the first function:
1)
f(x)=20-x
The inverse function is given as:
f(x)=y
20-x=y
i.e.
x=20-y
Hence, the inverse function satisfies the equation:
f(x)=20-x
2)
[tex]f(x)=\dfrac{x}{x-20}[/tex]
Now,
f(x)=y
[tex]\dfrac{x}{x-20}=y\\\\x=xy-20y\\\\xy-x=20y\\\\x(y-1)=20y\\\\x=\dfrac{20y}{y-1}[/tex]
Hence, the equation of inverse function is:
[tex]f(x)=\dfrac{20y}{y-1}[/tex]
Hence, the graph of inverse function has asymptotes at x=1 and also passes through (0,0).
3)
f(x)=20x
f(x)=y
20x=y
[tex]x=\dfrac{y}{20}[/tex]
so, the inverse function is:
[tex]f(x)=\dfrac{x}{20}[/tex]
Hence, the graph of this function is a straight line passing through (0,0)
4)
[tex]f(x)=\dfrac{x+20}{x}[/tex]
Let f(x)=y
[tex]\dfrac{x+20}{x}=y\\\\x+20=xy\\\\20=xy-x\\\\20=x(y-1)\\\\x=\dfrac{20}{y-1}[/tex]
