SOLUTION: I am having trouble with finding the domain for expressions like f(t)=log(t-5), g(x)=5e^x, g(x)=ln(x+4) and g(t)= 5^t. The concept eludes me, can anyone help with how to go about
Algebra.Com
Question 202690: I am having trouble with finding the domain for expressions like f(t)=log(t-5), g(x)=5e^x, g(x)=ln(x+4) and g(t)= 5^t. The concept eludes me, can anyone help with how to go about solving these??
E.T.
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the domain is the possible values that x can take.
the range is the possible values that y can take.
domain is possible values that x can take.
range is the possible values that y can take.
-----
your first problem:
f(t) = log(t-5)
you cannot take the log of any number that is 0 or less than 0.
your equation is y = log(t-5)
your domain is (t-5)
your range is log(t-5)
in this case (t-5) must be greater than zero which means that t must be > 5.
-----
your second problem is g(x) = ln(x+4).
same deal.
you cannot take the natural log of any number if it is 0 or less.
your equation is y = ln(x+4)
your domain is x+4 and your range is y which is ln(x+4)
your domain has to be > 0, so x+4 have to be > 0 which can only be if x > -4.
your domain is x > -4
-----
your third problem is g(x) = 5e^x
this is the same as y = 5e^x
x is your domain.
5e^x is your range.
in this particular case, there does not appear to be any restrictions to the value of x.
x can be any real number (negative, 0, or positive).
-----
your fourth problem is g(t) = 5^t.
this is the same as y = 5^t.
there do not appear to be any restrictions to the value of t, which is your domain.
t is your domain.
5^t is your range.
t can be any real number (negative, 0, or positive).
-----
exponents and logs are inverse relationships to each other.
if it wasn't for exponents, logarithms would not exist.
the rules are:
y = b^x if and only if x =
if y = b^x, the inverse function is y =
while x in the exponent equation can be any real number, x in the logarithm equation has to be > 0.
-----
in any equation, if y = f(x), x is the domain, and f(x) is the range.
-----
I hope this answers your quesation.
If it doesn't, send me an email with the specific area of discomfort, and I'll try to ease it for you.
RELATED QUESTIONS
Find the domain of the following:
a) f(t)=log(t-5)
b) g(x)=5e^x
c) g(x)=ln(x+4)
d)... (answered by edjones)
1) Find the domain of the following:
a) f(t)=log(t-5)
b) g(x)=5e
c)... (answered by stanbon)
Hello, Need help finishing my assignment. i am stuck on a domain question?
Find the... (answered by jim_thompson5910)
Can someone help me with these problems? Find the domain of the following.
Show how you... (answered by Fombitz)
Find the Domain of the following:
a) g(x) = 5^x
b) g(x) = In(x-4)
c) g(t) = log(t-2)... (answered by dhartman0220)
How do I find the domain of g(t)=log(t+2) and... (answered by Fombitz)
The problem states:
Find the domain of the following.
f(t)=log(t-5)
g(x)=5e xpower
(answered by stanbon)
Find the domain of the following:
g(x)=5^2
g(x)=1n(x-4)
g(t)=log(t+2)... (answered by edjones)
find the domain of the following: I need help I am so lost
f(t)=4.5e^t
g(x)=log(x+3)... (answered by stanbon)