Question

Find the domain of the function​

Answer 1

EXPLANATION.

→ Domain of the function.

→ f(x) = x² + 2x + 3 / x² - 5x + 6

→ For the domain denominator must be

greater than 0.

→ and x ≠ 0 For the function.

→ x² - 5x + 6 = 0 [ x ≠ 0 ]

→ x² - 3x - 2x + 6 = 0

→ x ( x - 3 ) - 2 ( x - 3 ) = 0

→ ( x - 2 ) ( x - 3 ) = 0

→ x = 2 and x = 3.

→ Domain of function f(x) = R - { 2,3}.

→ More information.

→ (1) Exponential function.

→ Let a ≠ 1 be a positive real number. Then,

f : R → ( 0 , ∞ ) defined by F(x) = a^x .

called exponential function.

→ Domain is R and range is ( 0,∞ )

→ (2) Logarithmic function.

→ Let a ≠ 1 be a positive real number. Then,

f : R → ( 0,∞ ) defined by

$\sf : \implies \: log_{e}x$

→ is called logarithmic function.

→ it's domain is ( 0 , ∞ ) and range is R