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A function f(x) is defined as f(x)=3x2−20x+c, where c is a constant. Also given f(1) = -16. What is the value of f(c) + f(-c) ?
- a)6
- b)8
- c)10
- d)12
- e)30
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
A function f(x) is defined as f(x)=3x2−20x+c, where c is a const...
Given Info:
- Function f(x) is given as f(x)=3x2−20x+c
- , where c is a constant
- The above function is a quadratic function in x
- Also given f(1)=−16
To Find:
- Value of f(c)+f(−c)
⇒f(c)+f(−c)=6c2+2c
Approach:
Working out:
- Now, f(c)=3c2−20c+c
- (Putting value of c in the given function → f(x)=3x2−20x+c
- And, f(−c)=3c2+20c+c
- Adding both functions, we get
⇒f(c)+f(−c)=3c2−20c+c+3c2+20c+c- Now in order to calculate the above value, we need to determine the value of c.
- To determine the value of c, we will work on the quadratic function in x. We know the value of function at x=1 as’ -16’ as given in the question, so we will calculate the value of c by putting the value of f(x) and the value of x.
- After knowing the value of c from the given value of the function at x=1, we will find the value of f(c)+f(−c)
- f(x)=3x2−20x+c
- Given f(1)=−16
⇒ f(1)=3(12)−20(1)+c
⇒ f(1)=c−17
- Now f(1)=−16
⇒ c−17=−16
⇒ c=1
- Now we have already established above, f(c)+f(−c)=6c2+2c
- Putting value of c from above, we get
⇒ f(c)+f(−c)=6(1)2+2(1)
⇒ f(c)+f(−c)=8
Answer
- So the value of f(c)+f(−c) is 8
- Hence answer option B is correct.
Most Upvoted Answer
A function f(x) is defined as f(x)=3x2−20x+c, where c is a const...
Given Information:
- Function f(x) = 3x^2 + 20x + c
- f(1) = -16
Calculating the value of c:
Given f(1) = -16
Substitute x = 1 into the function:
3(1)^2 + 20(1) + c = -16
3 + 20 + c = -16
23 + c = -16
c = -16 - 23
c = -39
Calculating f(c) and f(-c):
Substitute x = c into the function:
f(c) = 3c^2 + 20c + c
f(c) = 3(-39)^2 + 20(-39) - 39
f(c) = 3(1521) - 780 - 39
f(c) = 4563 - 780 - 39
f(c) = 3744 - 39
f(c) = 3705
Substitute x = -c into the function:
f(-c) = 3(-c)^2 + 20(-c) - 39
f(-c) = 3(39)^2 - 20(39) - 39
f(-c) = 3(1521) - 780 - 39
f(-c) = 4563 - 780 - 39
f(-c) = 3744 - 39
f(-c) = 3705
Calculating f(c) + f(-c):
f(c) + f(-c) = 3705 + 3705
f(c) + f(-c) = 7410
Therefore, the value of f(c) + f(-c) is 7410, which corresponds to option B.
- Function f(x) = 3x^2 + 20x + c
- f(1) = -16
Calculating the value of c:
Given f(1) = -16
Substitute x = 1 into the function:
3(1)^2 + 20(1) + c = -16
3 + 20 + c = -16
23 + c = -16
c = -16 - 23
c = -39
Calculating f(c) and f(-c):
Substitute x = c into the function:
f(c) = 3c^2 + 20c + c
f(c) = 3(-39)^2 + 20(-39) - 39
f(c) = 3(1521) - 780 - 39
f(c) = 4563 - 780 - 39
f(c) = 3744 - 39
f(c) = 3705
Substitute x = -c into the function:
f(-c) = 3(-c)^2 + 20(-c) - 39
f(-c) = 3(39)^2 - 20(39) - 39
f(-c) = 3(1521) - 780 - 39
f(-c) = 4563 - 780 - 39
f(-c) = 3744 - 39
f(-c) = 3705
Calculating f(c) + f(-c):
f(c) + f(-c) = 3705 + 3705
f(c) + f(-c) = 7410
Therefore, the value of f(c) + f(-c) is 7410, which corresponds to option B.
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