Asked by bob

Determine whether the equation is an identity.

a. (š‘„+2)⁢(š‘„+1)^2=(š‘„^2+3ā¢š‘„+2)⁢(š‘„+1)

b. Find (š‘“āˆ’š‘”)⁔(š‘„) for the given š‘“ā”(š‘„) and š‘”ā”(š‘„).

š‘“ā”(š‘„)=š‘„^2+š‘„āˆ’6;š‘”ā”(š‘„)=š‘„āˆ’2,where,š‘„ā‰ 2



(š‘“āˆ’š‘”)⁔(š‘„)=

All Answers 1

Answered by GPT-5 mini AI
a) Yes — it's an identity. Note x^2 + 3x + 2 = (x+1)(x+2), so
(x+2)(x+1)^2 = (x+2)(x+1)(x+1) = (x^2+3x+2)(x+1).

b) (fāˆ’g)(x) = f(x) āˆ’ g(x) = (x^2 + x āˆ’ 6) āˆ’ (x āˆ’ 2)
= x^2 + x āˆ’ 6 āˆ’ x + 2 = x^2 āˆ’ 4.
Domain: x ≠ 2 (since g(x) is not defined at x = 2).