Will give brainliest
Task 1
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 five values for each function. Graph the line y = x on the same graph.

Task 2
Part 1. Create two radical equations: one that has an extraneous solution, and one that does not have an extraneous solution. Use the equation below as a model:

a√x+b+c=d

Use a constant in place of each variable a, b, c, and d. You can use positive and negative constants in your equation.

Part 2. Show your work in solving the equation. Include the work to check your solution and show that your solution is extraneous.

Part 3. Explain why the first equation has an extraneous solution and the second does not.

TASK 1

Part 1

Let y=f(x)=(x+a)/b; x=g(y)=by-a=cy-d, so c=b and d=a.

Let d=a=2 and c=b=3: f(x)=(x+2)/3 and g(x)=3y-2.

Part 2

y=f(x)=(x+2)/3; 3y=x+2; x=3y-2=g(y) so g(x)=3x-2, the inverse.

Part 3

g(f(x))=3f(x)-2=3(x+2)/3-2=x+2-2=x, so g(f(x))=x showing that f(x) and g(x) are mutual inverses.

(Can’t graph)

TASK 2

Part 1

(a) Let a=1, b=2, c=3, d=6: √x+2+3=6; √x-6=-5; (b) Let a=-1, b=2, c=3, d=4

(a) Multiply both sides by √x+6: x-36=-5(√x+6)=-5√x-30; x-36+30=-5√x; x-6=-5√x.

Square both sides: x^2-12x+36=25x; x^2-37x+36=0=(x-36)(x-1).

Part 2

(a) So x=36 or 1 (apparently). Substitute x=36 in the original equation: 6+2+3=6, 11=6 is not true. So x=36 is an extraneous solution; substitute x=1: 1+2+3=6 is true, so x=1 is the actual solution.

(b) -√x+2+3=4; -√x=-1; multiply both sides by -1: √x=1; square both sides: x=1. Substitute x=1 in the original equation: -1+2+3=4 is true. So x=1 is the solution.

Part 3

For (a) the act of squaring both sides resulted in creating an extraneous solution ((-5)^2=25=5^2). For (b) the solution was simpler and there was no ambiguity.