Question

Let y = 2(x – 5)2 – 6.

Answer 1

The given equation represents a function and inverse of the function exist if x ≥ 6.

What is a function?

It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.

We have a function:

y = 2(x – 5)² – 6

Part A:

Using vertical line test, we can find the whether the graph is a function or not.

After drawing a graph for the given curve, and drawing a vertical line.

The vertical line touches only one point for the one input.

The given equation represents a function.

Part B:

Replace x → y and y → x

x = 2(y – 5)² – 6

2(y – 5)² = x + 6

$\rm y^-^1 = \sqrt{\dfrac{x+6}{2}} +5$

Plug x = 1 in the y:

y = 26

Plug  $\rm y ^-^1$ = 1 in inverse of a function:

x = 26

Thus, the given equation represents a function and inverse of the function exist if x ≥ 6.

Learn more about the function here:

brainly.com/question/5245372

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