Question

40 POINTS Match the one-to-one functions with the graphs of their inverse functions.

Answer 1

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)

$f(x)=\dfrac{x}{x-20}$

Now,

f(x)=y

$\dfrac{x}{x-20}=y\\\\x=xy-20y\\\\xy-x=20y\\\\x(y-1)=20y\\\\x=\dfrac{20y}{y-1}$

Hence, the equation of inverse function is:

$f(x)=\dfrac{20y}{y-1}$

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

$x=\dfrac{y}{20}$

so, the inverse function is:

$f(x)=\dfrac{x}{20}$

Hence, the graph of this function is a straight line passing through (0,0)

4)

$f(x)=\dfrac{x+20}{x}$

Let f(x)=y

$\dfrac{x+20}{x}=y\\\\x+20=xy\\\\20=xy-x\\\\20=x(y-1)\\\\x=\dfrac{20}{y-1}$

Answer 2

the first graph is (x+20)/x

the second graph is x/(x-20)