Find the domain for:
g(x)=5^x
g(x)=1n(x-4)
g(t)=log(t+2)
f(t)=5.5e^t
And what is your thinking on these?
From my thinking I would assume they are all real numbers except the last two
but I still can't say for sure
To find the domain for each of the given functions, we need to determine the set of all possible input values that can be used in the function.
1. g(x) = 5^x:
The domain for this function is all real numbers, since any real number can be raised to any exponent.
2. g(x) = ln(x - 4):
Since the natural logarithm (ln) is only defined for positive real numbers, the expression inside the logarithm, x - 4, must be greater than zero:
x - 4 > 0
Solving this inequality:
x > 4
Therefore, the domain for this function is all real numbers greater than 4.
3. g(t) = log(t + 2):
Similar to the previous function, the logarithm function is only defined for positive real numbers. The expression inside the logarithm, t + 2, must be greater than zero:
t + 2 > 0
Solving this inequality:
t > -2
Thus, the domain for this function is all real numbers greater than -2.
4. f(t) = 5.5e^t:
Exponential functions, represented here by e^t, are defined for all real numbers. Therefore, the domain for this function is also all real numbers.
To summarize:
1. g(x) = 5^x: Domain is all real numbers.
2. g(x) = ln(x - 4): Domain is x > 4.
3. g(t) = log(t + 2): Domain is t > -2.
4. f(t) = 5.5e^t: Domain is all real numbers.