Range of function

Algebra Level 2

Let f : R → R f : \mathbb{R} \to \mathbb{R} be a function where its range is ( a , + ∞ ) ) (a, +\infty)) . Define the function g : R → R g : \mathbb{R} \to \mathbb{R} such that g ( x ) = f ( x ) − 4 g(x) = f(x) - 4 for all x ∈ R x \in \mathbb{R} . What is the range of g g ?

( a − 4 , + ∞ ) (a-4, +\infty) None of these ( a , + ∞ ) (a, +\infty) ( a + 4 , + ∞ ) (a+4, +\infty)

Aman Joshi by Aman Joshi , 18, India

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1 solution

Aman Joshi
Nov 3, 2017

If the range of f is given by the interval (a , +infinity), we can write the following inequality f(x) > a add - 4 to both sides on the inequality to obtain f(x) - 4 > a - 4 The last inequality suggests that the range of f(x) - 4 is (a - 4, +infinity)

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