The problem does not specify what parts (a)-(d) mean.
I'll solve only the request that concerns the domain of given functions, assuming that `f(x)=2x^2 + 3` and `g(x) = 3x - 5` .
I'll start with `f(x) = 2x^2 + 3` . You need to remember that the domain of a function contains all possible x values for function f(x) to make sense.
Since the equation of this function may be solved under any condition, hence the domain of function is the real set of numbers. The range of function contains all f(x) values and for this situation, the range contains all real positive values, larger or equal to 3.
The domain of the next function `g(x)=3x - 5 ` is also the real set of numbers since the equation of the function, `3x-5 = g(x)` may be solved for any real value of x.
Hence, the domain of both functions `f(x)=2x^2 + 3` and `g(x) = 3x - 5` is the real set of numbers R.
The domain of f(x)=2x^2+3 is the real numbers. The range is all numbers >=3
The domain of f(x)=3x-5 is the real numbers. The range is all real numbers.
I do not understand what you mean by (a)-(d)?