Question

If f(x)=(x2-x)/(x2+2x), the range of f:

Answer 1

$\green{ \underline \ \bold{given : ( x2- x) \div ( x2 + 2x) }} \\ \tt : = > \: 2x - x \div 2x + 2x \\ \tt : = > 2x \div 4x \\ \tt : = > x = \frac{4}{2} = 2 \\ \tt : = > x = 2 \\ \tt : x = 2 \: is \: the \: range \: of(f)$

Answer 2

Answer:

Given f(x)=2−∣x−5∣

Domain of f(x) is defined for all real values of x.

Since, ∣x−5∣≥0⟹−∣x−5∣≤0

⟹2−∣x−5∣≤2⟹f(x)≤2

Hence, range of f(x) is (−∞,2].