Math Questions ?

Let y=f(x)be a function with domain D=(-inf,inf) and R=[-5, inf). Find the domain D and range R for the following functions and enter your answers using interval notation. 

a)1/2f(-x)+3
Domain: (-inf,inf)
Range: ?

az_lender2021-03-20T01:15:13Z

I assume that means (1/2)*f(-x) + 3.
The change from f(x) to f(-x) has no effect on the domain and no effect on the range.  It simply reflects the graph across the y-axis, that is, horizontally.  The (1/2) would reduce the range from [-5,inf) to [-2.5,inf), but then the +3 changes the range from [-2.5,inf) to [+0.5,inf).

Answer: D = (-inf,inf), R = [+0.5,inf).