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The given equation represents a function and inverse of the function exist if x ≥ 6.
<h3>What is a function?</h3>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
Plug x = 1 in the y:
y = 26
Plug = 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:
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