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Answer the following.
f(x) = x² + 2x - 3 for x ≥ -1. Given that the minimum value of x² + 2x - 3 occurs when x = -1…
$f(x) = x^2 + 2x - 3$ for $x \ge -1$.
Given that the minimum value of $x^2 + 2x - 3$ occurs when $x = -1$, explain why $f(x)$ has an inverse.
Answer
Answer
Official answer keyIt is a one-one function because the function is always increasing for the given restricted domain. Reason-we are told that the function has a domain of $x \geqslant -1$. So, it is only half of a quadratic graph. This means that we have a one-one function, since every point $y$ will only have one value of $x$. It is also onto. Since one-one and onto functions are invertible, the given function is also invertible.