Answer:
f(x-1) = (3/4)x² - (5/2)x + 7/4
Explanation:
To find f(x-1), we need to replace x by (x-1) on the equation of f(x), so
[tex]\begin{gathered} f(x)=\frac{3}{4}x^2-x \\ f(x-1)=\frac{3}{4}(x-1)^2-(x-1) \end{gathered}[/tex]Then, we can simplify the polynomial
[tex]\begin{gathered} f(x_{}-1)=\frac{3}{4}(x^2-2x+1)-x+1 \\ f(x-1)=\frac{3}{4}x^2-\frac{3}{4}(2x)+\frac{3}{4}-x+1 \\ f(x-1)=\frac{3}{4}x^2-\frac{3}{2}x-x+\frac{3}{4}+1 \\ f(x-1)=\frac{3}{4}x^2-\frac{5}{2}x+\frac{7}{4} \end{gathered}[/tex]Therefore, the simplified polynomial for f(x-1) is
f(x-1) = (3/4)x² - (5/2)x + 7/4
