Question

find
the domain of F(x) = x² 3x + 4/
x^2-5x+4​

Answer 1

Answer:

Domain value of function f(x)f(x) is (1,4)(1,4) .

Step-by-step explanation:

Given,

Domain of the function f(x)=\frac{x^{2}+3x+5}{x^{2}-5x+4}f(x)=

x

2

−5x+4

x

2

+3x+5

∴ f(x)=\frac{x^{2}+3x+5}{x^{2}-5x+4}=\frac{p(x)}{q(x)}f(x)=

x

2

−5x+4

x

2

+3x+5

=

q(x)

p(x)

If q(x)=0q(x)=0 then the above function f(x)f(x) can't be defined.

So, x^{2} -5x+4=0x

2

−5x+4=0

⇒x^{2} -4x-x+4=0x

2

−4x−x+4=0

⇒x(x-4)-(x-4)=0x(x−4)−(x−4)=0

⇒(x-1)(x-4)=0(x−1)(x−4)=0

∴ x=1,4x=1,4