Let f of x is equal to e to the x th power and g of x is equal to x minus 3 What are the domain and range of open paren f circ g close paren times x ?

The composition is (f ∘ g)(x) = f(g(x)) = e^(x−3). Since x−3 is defined for every real x, the domain is all real numbers. An exponential expression e^(x−3) is always greater than 0, so the range is y > 0, matching “domain: all real numbers; range: y is greater than 0.”

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