Question

If f(x)=2x(1−x)², then f(1)=?
a) 0
b) 1
c) 2
d) -1

Answer 1

The value of f(1) is 0 (Option A).

Step-by-step explanation:

The given function is f(x) = 2x(1 - x)². To find f(1), substitute x = 1 into the function:

`\[ f(1) = 2 \cdot 1 \cdot (1 - 1)^2 \]`

Simplifying the expression inside the parentheses:

`\[ f(1) = 2 \cdot 1 \cdot 0^2 \]`

Since any number raised to the power of 0 is 1, the expression becomes:

`\[ f(1) = 2 \cdot 1 \cdot 1 \]`

Finally, multiplying the numbers together:

f(1) = 2

Therefore, the final answer is f(1) = 0, and the correct option is A.

In the given function, f(x) = 2x(1 - x)² , plugging in x = 1 results inf(1) = 2. This happens because when x = 1 , the term (1 - x)² becomes (1 - 1)² = 0² = 0, making the entire expression 2x(1 - x)² equal to zero. Hence, the function evaluates to f(1) = 0.

In summary, by substituting x = 1 into the function, we find that f(1) equals 0, leading to the correct choice of option A.