Given: A function-
[tex]f(x)=4\sqrt{2x-1}+3[/tex]
Required: To determine the point where the function starts.
Explanation: To determine where the function starts, we need to determine the domain and range of the function. The domain of a function is the set of x values for which the function is defined.
The square root is not defined for negative values. Hence the domain of the function is the set of all x values greater than or equal to zero as follows-
[tex]\begin{gathered} \sqrt{2x-1}\ge0 \\ 2x\ge1 \\ x\ge\frac{1}{2} \\ Domain=[\frac{1}{2},\infty) \end{gathered}[/tex]
And the range for a function of the type-
[tex]c\sqrt{ax+b}+k[/tex]
is-
[tex]f(x)\ge k[/tex]
Hence, the range of the function is-
[tex][3,\infty)[/tex]
Hence, the function starts at the point (1/2,3).
Final Answer: Option D is correct.
