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)
$x^2 - 5$
$x^2 + 2x - 5$
$x^2 - 2x + 1$
$x^2 - 4$

Explanation:

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

$f(g(x)) = f(x-1) = (x-1)^2 + 2(x-1) - 4$

Step2: Expand squared term

$(x-1)^2 = x^2 - 2x + 1$

Step3: Expand linear term

$2(x-1) = 2x - 2$

Step4: Combine all terms

$x^2 - 2x + 1 + 2x - 2 - 4$

Step5: Simplify the expression

$x^2 + (-2x+2x) + (1-2-4) = x^2 - 5$

Answer:

$x^2 - 5$ (Option A)