Question

Drag the tiles to the correct boxes to complete the pairs.
Match the one-to-one functions with the graphs of their inverse functions.

Answer 1

Answer:

Part 1) The graph in the attached figure N 1

Part 2) The graph in the attached figure N 2

Part 3) The graph in the attached figure N 3

Part 4) The graph in the attached figure N 4

Step-by-step explanation:

Part 1) we have

$f(x)=20-x$

Find the inverse

Let

y=f(x)

$y=20-x$

Exchange the variables x for y and y for x

$x=20-y$

isolate the variable y

$y=-x+20$

$f^{-1}(x)=y$

$f^{-1}(x)=-x+20$ ------> inverse function

see the attached figure N 1

Part 2) we have

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

Find the inverse

Let

y=f(x)

$y=\frac{x}{x-20}$

Exchange the variables x for y and y for x

$x=\frac{y}{y-20}$

isolate the variable y

$y=\frac{20x}{x-1}$

$f^{-1}(x)=y$

$f^{-1}(x)=\frac{20x}{x-1}$ ------> inverse function

see the attached figure N 2

Part 3) we have

$f(x)=20x$

Find the inverse

Let

y=f(x)

$y=20x$

Exchange the variables x for y and y for x

$x=20y$

isolate the variable y

$y=\frac{1}{20}x$

$f^{-1}(x)=y$

$f^{-1}(x)=\frac{1}{20}x$ ------> inverse function

see the attached figure N 3  

Part 4) we have

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

Find the inverse

Let

y=f(x)

$y=\frac{x+20}{x}$

Exchange the variables x for y and y for x

$x=\frac{y+20}{y}$

isolate the variable y

$y=\frac{20}{x-1}$

$f^{-1}(x)=y$

$f^{-1}(x)=\frac{20}{x-1}$ ------> inverse function

see the attached figure N 4