Question

suppose $f(x) = (x - 3)^2 - 3$.
a) evaluate $f(0)$.

b) evaluate $f(1)$.

c) if $f(x) = 0$, what is $x$? separate answers with a comma.

d) if $f(x) = -2$, what is $x$? separate answers with a comma.

Explanation:

Part (a)

Step1: Substitute \( x = 0 \) into \( f(x) \)

Substitute \( x = 0 \) into \( f(x)=(x - 3)^2-3 \), we get \( f(0)=(0 - 3)^2-3 \).

Step2: Calculate the value

First, calculate \( (0 - 3)^2=(-3)^2 = 9 \), then \( f(0)=9 - 3=6 \).

Step1: Substitute \( x = 1 \) into \( f(x) \)

Substitute \( x = 1 \) into \( f(x)=(x - 3)^2-3 \), we get \( f(1)=(1 - 3)^2-3 \).

Step2: Calculate the value

First, calculate \( (1 - 3)^2=(-2)^2 = 4 \), then \( f(1)=4 - 3 = 1 \).

Step1: Set up the equation

Set \( f(x) = 0 \), so \( (x - 3)^2-3=0 \).

Step2: Solve for \( x \)

Add \( 3 \) to both sides: \( (x - 3)^2=3 \). Take square roots: \( x - 3=\pm\sqrt{3} \). Then \( x = 3\pm\sqrt{3} \).

Answer:

\( 6 \)

Part (b)