Let y = 2(x – 5)2 – 6. Part A: Is the given relation a function? Is it one-to-one? Explain completely. If it is not one-to-one, determine a possible restriction on the domain such that the relation is one-to-one. (5 points)

Part B: Determine y–1. Show all necessary calculations. (5 points)

Part C: Prove algebraically that y and y–1 are inverse functions. (5 points)

Step-by-step explanation:

this relation is indeed a function. this is the equation of a line with slope 4 and -26 as the y-intercept. when we drop a vertical line down through the graph through the x-axis, this vertical line touches the graph at exactly one place this is the definition of a function.

this function is also one to one. when we draw a horizontal line through the y-axis it touches the graph at exactly one place giving us one value of y for every one value of x

part B

part C

correct answer is infinitely many solutions

step-by-step explanation:

2(2x + 3) = -4 + 2(2x + 5)

solving the above equation:

4x + 6 = -4 +4x +10

combining like terms

4x -4x = -4+10-6

0=0

since both sides are 0=0, we end up into true statement it means it has infinite many solutions.

so correct answer is infinitely many solutions

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