Question

what is the range of the function f(x) = x+1/x+2​

Answer 1

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To find :

Range of function y=

1+x

2

x

Range is given by 'R'

Say f(x) = y

y=

1+x

2

x

y(1+x

2

)=x

y+yx

2

−x=0

yx

2

−x+y=0

x=

2a

−b±

b

2

−4ac

[∵ quadratic formula

and the sol

n

of x are real when

b

2

−4ac⩾0

so like wire

(

−1)−4(y)(y)⩾0

we solve the inequality for the values set of value of y.

1−4y

2

⩾0

1−4y

2

⩾0

1

2

−(2y)

2

⩾0

(1−2y)(1+2y)⩾0

(2y+1)(2y−1)⩽0 [Taking negative common]

(2y+1)⩾0 & (2y−1)⩽0

y⩾−1/2y⩽1/2

−1/2⩽y⩽1/2

so the range of y is [

2

1

,

2

−1

].