math question 1a?

Question

find the domain of the following:

f (t)=4.5e^t


g (x)=log(x+3)


g(x)=2^x


g (t)=ln (t-1)

thank you

Answer 1

The domain of a function is any value of the independent variable for which the value of the function is defined.

f(t) = 4.5e^t is defined for all real t because an exponential function is defined for any real value of the exponent.

g(x) = log(x + 3) is defined only for x + 3 > 0 ==> x > -3 because a logarithmic function (which includes ln) is defined only for arguments greater than zero.

The last two examples are solved using these same methods.

Answer 2

the domation of a log^a b is this
a should be allways more than 0 and b should allways be moe than 0 and it shouldnt be 1
so log (x+3) a=x+3 b=10
x+3>0 --> x>-3 10>0 its right and its not 1
Dg: x>-3

ln (or Ln) is log (e) (e is neper number)
Ln (t-1)= log e(t-1)= log e + log (t-1)
1) e>0 its right
2) t-1>0 --> t>1
Dg= 1U2 --> Dg: t>1

g(x)= 2^x Dg: R becuz u can place any number in place of x and it allways answers right:

2^2=4 2^ 1/2 =radical 2
2^-1 = 1/2
2^radical 2= 2^ 2^1/2

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Answer 3

f(t) = 4.5e^t has domain of all reals.

g(x) = log(x+3) has domain d > -3

g(x) = 2^x has domain of all reals

g(t) = ln(t-1) has domain t > 1