Question

expressions and equations
question 7 / 14
11-
for which value of x does f(x + 3) = -3?
select one answer
a -7
b -4
c -3
f(x) = x² + 4x

Explanation:

Step1: Substitute $x+3$ into $f(x)$

$f(x+3)=(x+3)^2 + 4(x+3)$

Step2: Expand and simplify the expression

$f(x+3)=x^2+6x+9+4x+12=x^2+10x+21$

Step3: Set equal to -3 and rearrange

$x^2+10x+21=-3 \implies x^2+10x+24=0$

Step4: Factor the quadratic equation

$(x+4)(x+6)=0$

Step5: Solve for $x$

$x+4=0 \implies x=-4$; $x+6=0 \implies x=-6$
(Note: $-6$ is not an option, so we use $x=-4$)

Answer:

B. -4