Question

I really need help!
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.

Answer 1

the inverse of a function, if there is one, flips the thing or mirrors it over the slant line y=x

so for each point you can let y=x

Answer 2

for example for
y= f(x) = x +a*b
change the y and x, solving that will give you the reflection, inverse function f^(-1)

x = y + a*b
y = x - a*b

inverse f^(-1)(x) = x - a*b

Answer 3

so i put in what ever number like f(x)=5+2/3 and do i repeat the same numbers in g(x)=cx−d

Answer 4

oh i see, f(x) = (x+a)/b

Answer 5

inverse of that, change x and y around and resolve that for y

x = (y+a)/b

b*x = y + a

y = b*x - a f^(-1)(x)
that is the inverse

f^(-1)(x) = bx - a

Answer 6

g(x) is cx - d

g(x)=cx - d

looks to be the same form, ig b=c and a=d

Answer 7

thank i think i get it

Answer 8

thank u not i sorry