Question

Which function has the same range as f(x)=−2/x-3+8?

a) g(x)=x−3−8
b) g(x)= x−3+8
c) both a and b
d) none of the above

Answer 1

The function f(x) = −2/(x-3)+8 has the same range as the function g(x) = x-3+8, which is option b) g(x) = x-3+8.

Step-by-step explanation:

The function f(x) = −2/(x-3)+8 has the same range as the function g(x) = x-3+8, which is option b) g(x) = x-3+8.

To determine this, we need to find the range of f(x) by analyzing the behavior as x approaches positive infinity and negative infinity. As x approaches positive infinity, the function approaches 8, which is the upper bound of the range. As x approaches negative infinity, the function also approaches 8, so 8 is also the lower bound of the range. Therefore, the range of f(x) is (8, 8), which is the same as the range of g(x).