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