Question

If f (x)=min (x^2,x,sgn (x^2+4x+5)) then the value of f (2) is equal to​

Answer 1

Step-by-step explanation:

sgn(x)=

x

∣x∣

The given function is f(x)=sgn(x

2

−2x+3)=

x

2

−2x+3

∣x

2

−2x+3∣

The nature of quadratic function is given as

b

2

−4ac

⟹2

2

−4(1)(3)

⟹4−12

⟹−8<0

impliesa>0b

2

−4ac<0

So the quadratic equation is always positive

f(x)=sgn(x

2

−2x+3)=

x

2

−2x+3

∣x

2

−2x+3∣

=

x

2

−2x+3

x

2

−2x+3

=1