Answer:
True - [tex]R=(5,\infty) , y|y>5[/tex]
Step-by-step explanation:
Given : The range of the function given below is the set of all positive real numbers greater than 5 , [tex]f(x)=5+4^x[/tex]
To find : The given statement is true or false?
Solution :
Domain of the function is where the function is defined
The given function [tex]f(x)=5+4^x[/tex] is an exponential function
So, the domain of the function is,
[tex]D=(-\infty,\infty) , x|x\in \mathbb{R}[/tex]
i.e, The set of all real numbers.
Range is the set of value that corresponds to the domain.
Let [tex]y=5+4^x[/tex]
If [tex]x\rightarrow \infty , y\rightarrow 5[/tex]
If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]
So, The range of the function is
[tex]R=(5,\infty) , y|y>5[/tex]
Therefore, The given statement is true.
