Question

Using the two functions listed below, insert numbers in place of letters A,b,c and d so that f(x) and g(x) are inverse

Answer 1

what are the two functions...?

Answer 2

stull need help?

Answer 3

Here is the full 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.

Answer 4

@BlooooooBlahBLIIIIK

Answer 5

@rheaanderson341

Answer 6

hmmm have you covered inverse functions yet?

Answer 7

Yes @jdoe0001

Answer 8

hmmm need to dash in a bit


but hmm what I'd do is, pick two random values for "a" and "b"
say 2 and 3
so f(x) = x+ab
f(x) = x+(2 * 3)
f(x) = x +6

Answer 9

so, if we use 2 and 3 for "a" and "b"

we end up with a function in "x" terms

so to find f(x), or "y"
we can simply use some "x" value, say 4

f(x) = x +6
x=4
f(x) = 4+6
f(4) = 10

Answer 10

Wait

Answer 11

It's f(x)=x+a/b

Answer 12

so... all that is thus far f(x) only
BUT
recall that the domain of one function, is the range of the inverse function
that is

if we use x= 4, as INPUT, and our OUTPUT is 10
then the inverse would have to take in, 10 and output 4

Answer 13

So y=x+2/3?

Answer 14

yes... using a/b

then get a random value for "x", to get some "y"

Answer 15

Okay so would that be the inverse function for fx?

Answer 16

so you get some OUTPUT from some INPUT

and reverse that on g(x)
IF g(x) is to be the inverse function, the OUTPUT of f(x), will serve as the INPUT for g(x)

Answer 17

and if you use those INPUT and OUTPUT values from f(x)
into g(x)

you can then solve for either "c" or "d"
and use a random "d", to get a "c", or the other way around

and g(x) will end up being the inverse
because of the INPUT and OUTPUT swap

Answer 18

anyhow... dashing :)

Answer 19

Okay.... So how would I get the equations