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1. Find the domain for each of the following.

(a) y = 1/x²-3x
(b) y = x/√2-x
(c) y = In(9-x²)
(d) y =√x/ 1+x²
(e) y = 2-√6-x
(f) y = 2²ˣ⁺³+1
(g) y=-2|x+3|-1
(h) y=2x³-3x²+x+11
(i) y = √(x-√x)

1 Answer

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To find the domain of a function, we need to consider any restrictions on the input values that would make the function undefined. For example, if there is a denominator in the function, we need to exclude any values of x that would make the denominator zero.

Here are the domains for each of the following functions:

(a) y = 1/x²-3x
The domain is all real numbers except 0 and 3.

(b) y = x/√2-x
The domain is all real numbers except 2.

(c) y = In(9-x²)
The domain is all real numbers between -3 and 3.

(d) y =√x/ 1+x²
The domain is all real numbers greater than or equal to 0.

(e) y = 2-√6-x
The domain is all real numbers less than or equal to 6.

(f) y = 2²ˣ⁺³+1
The domain is all real numbers.

(g) y=-2|x+3|-1
The domain is all real numbers.

(h) y=2x³-3x²+x+11
The domain is all real numbers.

(i) y = √(x-√x)
The domain is all real numbers greater than or equal to 0.

I hope this helps! Let me know if you have any other questions.

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