Question

How Find the domain of the function???
please help........
a. f(x)= 2x, -1 ≤x≤5

b. f(x)= 7/(2x+2)

c. g(x)= (x+10)/(x^2-4)

d. h(x)= √(10&x^2-6x)

e. H(x)= (x^2- 25)/(x+5)

Answer 1

if the value of function becomes 0/0 , 1/0 , infinity/infinity etc for any x then that x valu will not be included in the domain.
eg:-
b. f(x)=7/(2x+2)
if x = -1 then fx) = 7/0 so the domain would be all real numbers except minus one

Answer 2

thanks.

Answer 3

how about h(x)= √(10&x^2-6x)?

Answer 4

the value inside √ couldnt be <0 .

Answer 5

so what is it exactly?

Answer 6

The domain of a function is the the set of values that can be used for the x variable.

Answer 7

A polynomial function has no restrictions on x, so for any polynomial function, the domain is all real numbers.

Answer 8

can u show the solutions? pls.

Answer 9

A polynomial function is y equals a polynomial in x.
Eamples of ploynomial functions:
\(y = x + 3\)
\(y = 4x\)
\(y = x^4 - 8x^3 + 2x^2 - 6x + 7\)

Answer 10

can u show the solution for this one? h(x)=√(10&x^2-6x)

Answer 11

Where you need to look carefully to find the domain is when the function has a square root, since the radicand can't be negative. That means that the values of x that make the radicand negative have to be excluded from the domain.
Also, if there is a denominator in the function, any value of x that will make the denominaotr negative also has to be excluded.

Answer 12

With the above in mind, let's go through your problems.

Answer 13

yeah

Answer 14

a. f(x) = 2x
This is a polynmomial function. There is no value of x that will cause a problem, so the domain is all real numbers.

Answer 15

get it.

Answer 16

b. f(x)= 7/(2x+2)
Here you have a denominator. The problem is that a denominator can't equal zero. All values of x are in the domain except any value of x that will make the denominator zero.
To find out which values of x have to be excluded, we set the denominator equal to zero and solve for x.
2x + 2 = 0
2x = -2
x = -1
If x = -1, then 2x + 2 = 2(-1) + 2 = -2 + 2 = 0
Since x = -1 causes the denominator to be zero, then that value of x has to be excluded from the domain.
The domain is all real numbers ecept for x = -1.

Answer 17

c. g(x)= (x+10)/(x^2-4)
Here we have a denominator again.
Once again we set the denominator equal to zero and solve for x.

Answer 18

\(x^2 - 4 = 0\)
To solve for x, we factor the left side:
\( (x + 2)(x - 2) =0 \)
\(x + 2 = 0\) or \(x - 2 = 0\)
\(x = -2\) or \(x = 2\)
Since -2 and 2 are the values of x that make a zero denominator, they can't be in the domain.
The domain is all real numbers except -2 and 2.

Answer 19

so for letter a, the domain is just all real numbers?

Answer 20

Yes

Answer 21

if x-2
g(x)=undefined

Answer 22

is there any solutions for letter a?

Answer 23

basically the numbers that makes the equation undefined is what you cannot have like for g(x)=(x+20)/(x^2-4)

Answer 24

yep there's no solution there .

Answer 25

d. h(x)= √(10&x^2-6x)
In this case, you don't have a denominator, but you have a square root.
The square root of a negative number is not real, so we have to see which values of x will make the radicand nonnegative.

First, what is the "&" doing in there?
Is this supposed to be
\(h(x) =\sqrt{10x^2 - 6x}\) ?

Answer 26

its h(x)= 10√(x^2-6x) actually.

Answer 27

This?
\(h(x) =10\sqrt{x^2 - 6x}\)

Answer 28

so there's no solution for letter a? the answer is just "the domain is all real numbers?

Answer 29

yes that's it.

Answer 30

I thought the answer for letter a is that the domain is all real numbers except 3/5.

Answer 31

For a. the answer is "all real numbers"

Answer 32

ok thanks

Answer 33

Wait. I have a question on a.

Answer 34

go on

Answer 35

a. f(x)= 2x, -1 ≤x≤5

Answer 36

For a. it states above:
a. f(x)= 2x, -1 ≤x≤5

Is this "-1 ≤ x ≤ 5" part of the problem ?

If so then that is the domain.

Answer 37

yes it is part of the problem.

Answer 38

so whats the final answer for a?

Answer 39

Ok, then the answer for a. is "the domain is -1 ≤ x ≤ 5"

Answer 40

can u show me the solution for letter a pls?

Answer 41

Normally, the domain of f(x) = 2x is all real numbers.
In this case, you are told that the domain is -1 ≤ x ≤ 5 when you are given the problem.
Answer for a. "the domain is -1 ≤ x ≤ 5"

Answer 42

alright, thanks.

Answer 43

b. amd c. are already answered above.

Answer 44

so there is no solutions anymore for letter a?

Answer 45

No, that is it: -1 ≤ x ≤ 5

Answer 46

ok. so whats the domain for letter d and e?

Answer 47

For d., you need to see for which values of x the radicand is nonnegative. That is the domain.
We need to solve the inequality
\(x^2 - 6x \ge 0\)

Answer 48

yeah.

Answer 49

To solve this inequality, first look at its corresponding equation:
\(x^2 - 6x = 0\)
We solve it by factoring the left side:
\(x(x - 6) =0 \)
x = 0 or x - 6 = 0
x = 0 or x = 6
The solution to the corresponding equation is x = 0 or x = 6.
We need the solution tot he inequality, \( x^2 - 6x \ge 0\),
so we draw a number line and plot 0 and 6.