PLEASE! Find the domain and range 1. y=(3x+1)/√(x^2+x-2) and 2. (5x-3)/(2x+1)?

Question

PLEASE help me and show how you found that answer, my summer homework is due on tuesday and I am just stumpped on how to find this.

The most detailed yet simplistic answer will win best answer and 5 stars

Thanks again!!

Answer 1

1. y=(3x+1)/√(x^2+x-2)

(x^2+x-2)  >= 0

(x+2)(x-1) >= 0

x+2>= 0

x>= -2

x-1 >= 0

x >= 1

all real numbers such that x >=-2 and x is not equal to 1

and 2. (5x-3)/(2x+1)?

Answer 2

For the domain's restriction, look at the denominator.

1.

x² + x - 2 > 0

(x + 2)(x - 1) > 0

There are two cases.

i) x + 2 > 0 and x - 1 > 0

x > -2 and x > 1

So x > 1

ii) x + 2 < 0 and x - 1 < 0

x < -2 and x < 1

So x < -2

The domain is x belongs to all real numbers where x < - 2 or x > 1.

The range is all real numbers.

2.

2x + 1 not equals to 0

2x not equals to -1

x not equals to -1/2

The domain is x belongs to all readl numbers where x is not equals to -1/2.

The range is all real numbers.