Question

find the range of
i) f(x) =3/2 -x^2
ii) f(x) = 3- |x-2|​

Answer 1

Answer:

i) f(x ) = 3/( 2 - x²)

y = 3/( 2 - x²)

2y -yx² = 3

x²y -2y + 3 = 0

x² =(2y -3)/y

x = ±√{( 2y -3)/y }

f( y) = ±√{(2y -3)/y}

domain of f( y) = range of f(x )

(2y -3)/y ≥0 ,

y ≥ 3/2 and y <0 and y ≠ 0

if y = 0

f(x ) = y = 3/(2 -x²) =0

3 ≠ 0

so, y ≠ 0

hence , range of f(x) € [ 3/2, ∞) U(-∞, 0)

Step-by-step explanation:

Answer 2

i) f(x) = (-∞, 3/2]

ii) f(x) = (-∞, 3]