Thanks you in advance..Find the domain of the following:?

Question

Find the domain of the following:?
a) f(t)=log(t-5)

Answer:

Show your work or explain how you obtained your answer here:

b) g(x)=5e^x

Answer:

Explain how you obtained your answer here:

c) g(x)=ln(t+4)

Answer:

Show your work or explain how you obtained your answer here:

d) g(t)=5^t

Answer:

Explain how you obtained your answer here:

Answer 1

a)
t-5 >0

t>5
so the domain is ] 5,∞[
<--------------->
b)
5e^x
domain all real numbers
<-------------->
c)
t+4>0
t>-4
domain ] -4 , ∞ [

<----------->
d)
5^t
all real numbers
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explanation , u must get log of +ve number

Answer 2

a) f(t)=log(t-5)

Answer: Log is defined for arguments > 0 (note log(0) is negative infinity).

Domain: {t | t - 5 > 0 or t > 5}

b) g(x)=5e^x

Answer: The exponential is defined for real numbers. Note e^(-2) = 1/e^2, e^0 = 1, and e^10 is, well e^10.

domain: {x | x is in R}


c) g(x)=ln(t+4)

Answer: see answer to (a) above.

d) g(t)=5^t

Answer: see answer to (b) above.

Answer 3

t>5 ( negative an 0 don´t have log
allreal
t>-4 the same as the first
all real as the base 5 is positive the power always exists

Answer 4

a) anything inside a log function must be positive, so:
t-5 = 0
t=5

therefore, the domain of this function is all real numbers greater than 5.

b) the exponential function can be all real numbers. there are no mathematical laws broken when you put negative x values in this function.

c) this is the exact same as (a).

t+4 = 0
t = -4

so, all real numbers greater than -4.

d) same as (b), all real numbers.