Part A:
The function f(x) = x^3 + x^2 - 2x + 3 is a polynomial function because it is a sum of terms where each term is a constant multiplied by a variable raised to a non-negative integer power.
The function g(x) = log(x) + 2 is a logarithmic function because it involves the logarithm of x.
Part B:
Domain of f(x):
The domain of f(x) is all real numbers because there are no restrictions on the values that x can take in the polynomial function.
Range of f(x):
To find the range of f(x), we need to analyze the behavior of the cubic function. Since the leading coefficient is positive, the function will increase without bound as x approaches positive infinity and decrease without bound as x approaches negative infinity. Therefore, the range of f(x) is all real numbers.
Domain of g(x):
The domain of g(x) is all positive real numbers because the logarithm function is only defined for positive values of x.
Range of g(x):
The range of g(x) is all real numbers because the logarithm function can output any real number depending on the input value.
In conclusion, both functions have domains that include all real numbers, but their ranges differ. The range of f(x) is all real numbers, while the range of g(x) is also all real numbers but restricted to positive values due to the nature of the logarithmic function.
here: do you have any other questions?
The functions f(x) = x3 + x2 – 2x + 3 and g(x) = log(x) + 2 are given.
Part A: What type of functions are f(x) and g(x)? Justify your answer.
Part B: Find the domain and range for f(x) and g(x). Then compare the domains and compare the ranges of the functions.
