Question

Find the range of the function f(x)=√x^2-7x+10

please help me out ​

Answer 1

Answer:

Step-by-step explanation:

We have,

$\tt{y=f(x)=\sqrt{x^2-7x+10}}$

$\sf{\implies\,y^2=x^2-7x+10}$

$\sf{\implies\,x^2-7x+10-y^2=0}$

Now,

Its discriminant will be positive,

$\sf{\implies\,(-7)^2-4\cdot1\cdot(10-y^2)\ge0}$

$\sf{\implies\,49-40+4y^2\ge0}$

$\sf{\implies\,9+4y^2\ge0}$

This is always true for all $\sf{x\in\mathbb{R}}$

But y must be positive because the square root function is always positive.

So,

$\sf{Range\,\,of\,\,f(x)\in[\,0,\infty)}$