Let f: R → R be given as f(x) = 4x² + 2, then value of f(1) equals?
Understand the Problem
The question is asking to calculate the value of the function f(x) = 4x² + 2 at x = 1. This involves substituting x with 1 into the given function and simplifying the expression to find the answer.
Answer
The value of \( f(1) \) is \( 6 \).
Answer for screen readers
The value of ( f(1) ) equals ( 6 ).
Steps to Solve
- Substitute the value of x into the function To find ( f(1) ), replace ( x ) in the function ( f(x) = 4x^2 + 2 ) with ( 1 ):
$$ f(1) = 4(1)^2 + 2 $$
- Calculate the square of 1 Calculating ( (1)^2 ):
$$ (1)^2 = 1 $$
- Multiply by 4 Now multiply by 4:
$$ 4 \times 1 = 4 $$
- Add 2 Finally, add 2:
$$ 4 + 2 = 6 $$
The value of ( f(1) ) equals ( 6 ).
More Information
This problem demonstrates how to evaluate a polynomial function by substituting a specific value for the variable, in this case, ( x = 1 ). The process involves basic arithmetic operations, including squaring, multiplication, and addition.
Tips
- Forgetting to square first: Ensure that you square the value of ( x ) before performing other operations.
- Misplacing parentheses: Miswriting the function or calculations can lead to incorrect results. Always check your substitutions and operations.
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