Domain of a composite function without having g(x) function
$begingroup$
Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
$f(3x^2)$ $f(1-x)$ and $f(sin x)$
I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?
sorry for my bad English
functions function-and-relation-composition
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
$endgroup$
add a comment |
$begingroup$
Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
$f(3x^2)$ $f(1-x)$ and $f(sin x)$
I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?
sorry for my bad English
functions function-and-relation-composition
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
$endgroup$
add a comment |
$begingroup$
Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
$f(3x^2)$ $f(1-x)$ and $f(sin x)$
I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?
sorry for my bad English
functions function-and-relation-composition
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
$endgroup$
Suppose that the domain of "$f$" function is equal to $[0,1]$, then find the domain of:
$f(3x^2)$ $f(1-x)$ and $f(sin x)$
I know that $f(3x^2)$ is the same that we say $g = 3x^2$ so it's domain is $R$
When we have $f$ and $g$ functions we can find simply the domain of $fog$ using function composition but how should we find the domain of $fog$ when we don't have $g$ function?
sorry for my bad English
functions function-and-relation-composition
functions function-and-relation-composition
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
asked Dec 24 '18 at 6:47
bashir sabooribashir saboori
61
61
add a comment |
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
Guide:
We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$
respetively since the output of $g$ needs to be a subset of domain of $f$.
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
$endgroup$
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Guide:
We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$
respetively since the output of $g$ needs to be a subset of domain of $f$.
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
$endgroup$
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
add a comment |
$begingroup$
Guide:
We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$
respetively since the output of $g$ needs to be a subset of domain of $f$.
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
$endgroup$
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
add a comment |
$begingroup$
Guide:
We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$
respetively since the output of $g$ needs to be a subset of domain of $f$.
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
$endgroup$
Guide:
We need the following conditions $$3x^2 in [0,1], 1-x in [0,1], sin x in [0,1].$$
respetively since the output of $g$ needs to be a subset of domain of $f$.
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
edited Dec 24 '18 at 7:54
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
answered Dec 24 '18 at 6:51
Siong Thye GohSiong Thye Goh
102k1468119
102k1468119
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
add a comment |
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
The range of $3x^2∈[0,1]$?
$endgroup$
– bashir saboori
Dec 24 '18 at 7:11
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
You have to find $x$ such that $0 le 3x^2 le 1, 0 le 1-x le 1, 0 le sin x le 1$.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:19
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
$begingroup$
It's possible for $x$ to be negative.
$endgroup$
– Siong Thye Goh
Dec 24 '18 at 7:55
add a comment |
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