Problem

Find the domain and range of the function f(x)=1x+3

Answer

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Answer

Step 2: To find the range, we need to consider the values that f(x) can take. Since f(x) is a rational function, it can take any real number value except 0. Thus, the range of the function is all real numbers except 0. In interval notation, the range is (−∞,0)∪(0,∞).

Steps

Step 1 ：Step 1: Set the denominator equal to zero and solve for x to find the values that are excluded from the domain. So, x+3=0 which implies x=−3. Thus, the domain of the function is all real numbers except −3. In interval notation, the domain is (−∞,−3)∪(−3,∞).

Step 2 ：Step 2: To find the range, we need to consider the values that f(x) can take. Since f(x) is a rational function, it can take any real number value except 0. Thus, the range of the function is all real numbers except 0. In interval notation, the range is (−∞,0)∪(0,∞).

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