If f(x)=3x^2-x+2 then
what is 2f(a)?
What is f(2a)?
What is f(a^2)?
What is [f(a)]^2?
What is f(a+h)?
2 f ( a ) = 2 ( 3 a ^ 2 - a + 2 ) =
6 a ^ 2 - 2a + 4
f ( 2a ) = 3 [ ( 2a ) ^ 2 ] - 2a+ 2 =
3 ( 4a ^ 2 ) - 2a + 2 =
12 a ^ 2 - 6 a + 6
f ( a ^ 2 ) = 3 [ ( a ^ 2 ) ^ 2 ] - a ^ 2 + 2 =
3 a ^ 4 - a ^ 2 + 2
[f ( a ) ] ^ 2 = ( 3 a ^ 2 - a + 2 ) ^ 2 =
9 a ^ 4 - 6 a ^ 3 +1 3 a ^ 2 - 4 a + 4
f ( a + h ) = 3 a ^ 2 + 6 a h - a + 3 h ^ 2 - h + 2
f ( a + h ) = 3 ( a + h ) ^ 2 - ( a + h ) + 2 =
3 a ^ 2 + 6 a h - a + 3 h ^ 2 - h + 2
To find the value of a given function for different inputs, you need to substitute the input value into the function and simplify the expression.
1. What is 2f(a)?
To find 2f(a), multiply the function f(a) by 2:
2f(a) = 2(3a^2 - a + 2)
= 6a^2 - 2a + 4
2. What is f(2a)?
To find f(2a), substitute 2a into the function:
f(2a) = 3(2a)^2 - (2a) + 2
= 3(4a^2) - 2a + 2
= 12a^2 - 2a + 2
3. What is f(a^2)?
To find f(a^2), substitute a^2 into the function:
f(a^2) = 3(a^2)^2 - (a^2) + 2
= 3a^4 - a^2 + 2
4. What is [f(a)]^2?
To find [f(a)]^2, square the value of f(a):
[f(a)]^2 = (3a^2 - a + 2)^2
= (3a^2 - a + 2)(3a^2 - a + 2)
= 9a^4 - 3a^3 + 6a^2 - 3a^3 + a^2 - 2a + 6a^2 - 2a + 4
= 9a^4 - 6a^3 + 13a^2 - 4a + 4
5. What is f(a+h)?
To find f(a+h), substitute (a+h) into the function:
f(a+h) = 3(a+h)^2 - (a+h) + 2
= 3(a^2 + 2ah + h^2) - a - h + 2
= 3a^2 + 6ah + 3h^2 - a - h + 2
These are the simplified expressions for each expression value based on the given function.