Answer:
Only p(x) has all real numbers as its domain
Step-by-step explanation:
The given functions is:
[tex]f(x)=2^{-x}[/tex]
g(x) = 5ˣ
p(x) = (1, 3) and (2, 12)
To find equation of the line passing through points (x₁,y₁) and (x₂,y₂), (x₁≠x₂). We use formula:
[tex]y-y_{1} =\frac{ y_{2}-y_{1}}{x_{2}-x_{1}}\times(x-x_{1})[/tex]
where,(x₁,y₁) = (1, 3) and (x₂,y₂) = (2,12)
Hence, p(x) = y = 9x − 6
Here, both f(x) and g(x) is exponential function and p(x) is linear function.
Also here f(x) is not defined in large negative value, hence its domain is not all real numbers.
And g(x) is not defined in large positive value, hence its domain is not all real numbers.
But p(x) is defined over all real numbers, hence Only p(x) has domain of all real numbers.
