# If the function f(x) has a domain of -2<=x<= 8 and a range of -4<= y <= 6 and the function g (x) is defined by the formula g(x)=5f(2x)) then what are the domain and range of g?

Use basic function transformations to find the new domain and range. $5 f \left(x\right)$ means that the function is vertically stretched by a factor of five.
Therefore, the new range will span an interval that is five times greater than the original. In the case of $f \left(2 x\right)$, a horizontal stretch by a factor of a half is applied to the function. Therefore the extremities of the domain are halved.