Question
35. What is the number of the intersection of the two functions \( f(x)=x \) and \( g(x)=x^{(2)} \) ? \( \begin{array}{llll}\text { (A) } 1 & \text { (B) } 2 & \text { (C) } 3 & \text { (D) } 4\end{array} \)
Ask by Boone Dunn. in Iraq
Mar 10,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The functions intersect at 2 points.
**Answer: (B) 2**
Solution
To find the intersection points, we set the two functions equal to each other:
\[
x = x^2
\]
Subtract \( x \) from both sides:
\[
x^2 - x = 0
\]
Factor the equation:
\[
x(x - 1) = 0
\]
Setting each factor equal to zero gives:
\[
x = 0 \quad \text{or} \quad x = 1
\]
Thus, the functions intersect at 2 points: when \( x = 0 \) and when \( x = 1 \). The correct answer is **(B) 2**.
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Simplify this solution Extra Insights
To find the number of intersections between the two functions \( f(x) = x \) and \( g(x) = x^2 \), we need to determine where these two functions are equal. Setting \( x = x^2 \) gives us the equation \( x^2 - x = 0 \), which factors to \( x(x - 1) = 0 \). Thus, the solutions are \( x = 0 \) and \( x = 1 \). Therefore, the two functions intersect at two points: \( (0, 0) \) and \( (1, 1) \). So, the number of intersections is \( \text{(B) } 2 \).
