Question

you will be asked to upload your handwritten work for questions 1 - 3.
given that $f(x)=x^2 + 2x - 4$ and $g(x)=x - 1$, find $f(g(x))$. show all steps.
(10 points)
$\bigcirc$ $x^2 - 4$
$\bigcirc$ $x^2 - 2x + 1$
$\bigcirc$ $x^2 + 2x - 5$
$\bigcirc$ $x^2 - 5$

Explanation:

Step1: Substitute $g(x)$ into $f(x)$

Replace $x$ in $f(x)$ with $g(x)=x-1$:
$f(g(x))=(x-1)^2 + 2(x-1) - 4$

Step2: Expand $(x-1)^2$

Use the formula $(a-b)^2=a^2-2ab+b^2$:
$(x-1)^2 = x^2 - 2x + 1$

Step3: Expand $2(x-1)$

Distribute the 2 to the terms inside:
$2(x-1)=2x-2$

Step4: Combine all terms

Substitute back and simplify:
$f(g(x))=x^2 - 2x + 1 + 2x - 2 - 4$
Combine like terms: $-2x+2x=0$, $1-2-4=-5$
$f(g(x))=x^2 - 5$

Answer:

$\boldsymbol{x^2 - 5}$ (matches the last option)