Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.

f(x)=
x+a
b

g(x)=cx−d

Part 2. Show your work to prove that the inverse of f(x) is g(x).

Part 3. Show your work to evaluate g(f(x)).

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

Question

Part 1. Using the two functions listed below, insert numbers in place of the letters a, b, c, and d so that f(x) and g(x) are inverses.

f(x)=
x+a
b

g(x)=cx−d

Part 2. Show your work to prove that the inverse of f(x) is g(x).

Part 3. Show your work to evaluate g(f(x)).

Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include 5 values for each function. Graph the line y = x on the same graph.

anonymous · Answer

$$f(x)=\frac{ x+a }{ b }$$$$g(x)=cx-d$$

anonymous · Answer

@waterineyes  can you help

anonymous · Answer

@iGreen ?

mathmath333 · Answer

put any two numbers for a and b

say a=1, b=2

$\large\tt \color{black}{f(x)=\dfrac{x+1}{2}}$
for finding inverse

$\large\tt \color{black}{y=\dfrac{x+1}{2}}$

$\large\tt \color{black}{2y=x+1}$

$\large\tt \color{black}{2y-1=x}$

swap x and y

$\large\tt \color{black}{2x-1=y}$

$\large\tt \color{black}{y=2x-1}$

$\large\tt \color{black}{g(x)=2x-1}$