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Mathematics, 01.12.2020 23:30 markrandsdenn

PLEASE HELP LOTS OF POINTS LOT Part 4. Graph your two functions on a coordinate plane. Include a table of values for each function. Include five values for each function. Graph the line y = x on the same graph.

here is what i have for parts 1 2 and 3. please help please PART 2 and 3 are together just so you know. Please 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
One is (a=6,b=2,c=1,d=3

Part 2. Show your work to prove that the inverse of f(x) is g(x) and PART 3 Show your work to evaluate g(f(x)).

If we want both functions to be equal, we need the terms to equal one to one. This is, term with x must be equal, and the independent term must also be equal. Let’s start with the terms that equal x. In f(x) we have simply x and in g(x) we have cx. We need than x to be equal to cx: x=cx. Here we have to possibilities: c=1x=x *1 x=x.
c=0 0=0 x =0x = 0=0
Then we need the independent terms to be equal: a/b=-d
Here we have the infinite combinations. For example, we could have a=6, b=2, and d=-3, so
a/b= 6/2=3
-d= -(-3) =3
So, for the set (a=6, b=2, c=1, and d=-3) we have
F(x)= x + a/b = x+6/2 = x+3
g(x) =1*x- (-3) = x+3
So, f(x) = G(x)= x+3

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