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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)
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Practice Questions
1 question
Q1
If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)
0, Yes
0, No
1, Yes
1, No
Show Solution
Copy
f(1) = 1^3 - 3*1 + 2 = 0. The function is a polynomial and hence continuous everywhere, including at x = 1.
Questions & Step-by-step Solutions
1 item
Q
Q: If f(x) = x^3 - 3x + 2, what is f(1)? Is f(x) continuous at x = 1? (2019)
Solution:
f(1) = 1^3 - 3*1 + 2 = 0. The function is a polynomial and hence continuous everywhere, including at x = 1.
Steps: 10
Show Steps
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.
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