Question

find the domain and range of the following:
y=x²-2x+5​

Answer 1

Answer:

Find the domain and range of the function y=1x+3−5 . To find the excluded value in the domain of the function, equate the denominator to zero and solve for x . So, the domain of the function is set of real numbers except −3 . The range of the function is same as the domain of the inverse function.

Answer 2

Most of teachers say you must complete, complete the square to solve problems like this.

But it can be solved by thinking outside the box, which is :

solving equation $x^2-2x+5-y=0$

Its domain is all over reals. For the solutions to be real, it is required that D≥0

Now it gets interesting. If we use D≥0

→ $4-4(5-y)\geq 0$

→ $4y-16\geq 0$ → $y\geq 4$

Since y is the function value, range will be y≥4 as it is.

I hope it helps. Thinking outside the box is fun. I hope you enjoyed.

Math is not memorizing, it is to understand. -Me-