If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)

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Question: If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)

Options:

Correct Answer: 1, Yes

Exam Year: 2019

Solution:

f(1) = 1^3 - 3*1 + 2 = 0. The function is a polynomial and hence continuous everywhere, including at x = 1.

If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)

If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)

Step 1: Identify the function given in the question, which is f(x) = x^3 - 3x + 2.
Step 2: To find f(1), substitute x with 1 in the function: f(1) = 1^3 - 3*1 + 2.
Step 3: Calculate 1^3, which is 1.
Step 4: Calculate -3*1, which is -3.
Step 5: Now, combine the results: f(1) = 1 - 3 + 2.
Step 6: Calculate 1 - 3, which is -2.
Step 7: Now add -2 and 2: -2 + 2 = 0.
Step 8: So, f(1) = 0.
Step 9: To check if f(x) is continuous at x = 1, note that f(x) is a polynomial function.
Step 10: Polynomial functions are continuous everywhere, including at x = 1.

Function Evaluation – The process of substituting a specific value into a function to find its output.
Continuity of Functions – Understanding that polynomial functions are continuous everywhere on their domain.