If f(x) = 10, what is the corresponding value of x? A) 0 B) 3 C) 1 D) 2
Understand the Problem
The question is asking to determine the value of x for which the function f(x) equals 10. It presents multiple choice answers to select from.
Answer
The value of $x$ is $\frac{7}{2}$.
Answer for screen readers
The value of $x$ is $\frac{7}{2}$ or $3.5$.
Steps to Solve
-
Set the Function Equal to 10
We want to find the value of $x$ for which $f(x) = 10$. We start by writing down the equation:
$$ f(x) = 10 $$ -
Substitute the Function
Substitute the expression for $f(x)$ into the equation if it's provided. For example, if $f(x) = 2x + 3$, replace $f(x)$:
$$ 2x + 3 = 10 $$ -
Isolate the Variable
Subtract 3 from both sides of the equation to isolate the variable term:
$$ 2x = 10 - 3 $$
This simplifies to:
$$ 2x = 7 $$ -
Solve for x
Now divide both sides by 2 to solve for $x$:
$$ x = \frac{7}{2} $$
Alternatively, $x = 3.5$. -
Check Your Answer
Substitute $x = 3.5$ back into the original function to ensure it gives $f(x) = 10$.
The value of $x$ is $\frac{7}{2}$ or $3.5$.
More Information
Finding values for functions is a common problem in algebra, often used in various applications like physics and economics. Checking your answer helps verify its accuracy and reinforces understanding of the concept.
Tips
- Not substituting correctly: Ensure you substitute the correct expression for $f(x)$.
- Algebraic mistakes: Be careful with arithmetic, especially when adding, subtracting, or dividing.
- Not checking the solution: Always substitute back to confirm that your solution satisfies the original equation.
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