Questions: Find F(3)= Find x if F(x)=-5. Find x if F(x)=1. Find F(-7) Find the minimum. Find the maximum. Find the domain. Find the range. Where is the function constant? What is the rate of change when x=-2 ? Where is the function decreasing? Where is the function increasing?

Find F(3)= Find x if F(x)=-5.

Find x if F(x)=1. Find F(-7)

Find the minimum. Find the maximum.

Find the domain. Find the range.

Where is the function constant? What is the rate of change when x=-2 ?

Where is the function decreasing? Where is the function increasing?
Transcript text: Find $F(3)=$ Find $x$ if $F(x)=-5$. Find $x$ if $F(x)=1$. Find $F(-7)$ Find the minimum. Find the maximum. Find the domain. Find the range. Where is the function constant? What is the rate of change when $x=-2$ ? Where is the function decreasing? Where is the function increasing?
failed

Solution

failed
failed

Solution Steps

Step 1: Find \( F(3) \)

To find \( F(3) \), we substitute \( x = 3 \) into the function \( F(x) \): \[ F(3) = 3^2 - 4 \cdot 3 + 3 = 0 \]

Step 2: Solve for \( x \) when \( F(x) = -5 \)

We set the equation \( F(x) = -5 \): \[ x^2 - 4x + 3 = -5 \] This simplifies to: \[ x^2 - 4x + 8 = 0 \] The solutions to this equation are: \[ x = 2 - 2i \quad \text{and} \quad x = 2 + 2i \]

Step 3: Solve for \( x \) when \( F(x) = 1 \)

We set the equation \( F(x) = 1 \): \[ x^2 - 4x + 3 = 1 \] This simplifies to: \[ x^2 - 4x + 2 = 0 \] The solutions to this equation are: \[ x = 2 - \sqrt{2} \quad \text{and} \quad x = 2 + \sqrt{2} \]

Final Answer

\( F(3) = \boxed{0} \)
\( x \) for \( F(x) = -5 \) are \( \boxed{2 - 2i} \) and \( \boxed{2 + 2i} \)
\( x \) for \( F(x) = 1 \) are \( \boxed{2 - \sqrt{2}} \) and \( \boxed{2 + \sqrt{2}} \)
\( F(-7) = \boxed{57} \)
Minimum: \( \boxed{1} \)
Maximum: \( \boxed{\infty} \)
Domain: \( \boxed{(-\infty, \infty)} \)
Range: \( \boxed{[1, \infty)} \)
Function is constant: \( \boxed{\text{none}} \)
Rate of change at \( x = -2 \): \( \boxed{-4} \)
Function is decreasing: \( \boxed{(-\infty, 2)} \)
Function is increasing: \( \boxed{(2, \infty)} \)

Was this solution helpful?
failed
Unhelpful
failed
Helpful