Asked by bob
Determine whether the equation is an identity.
a. (š„+2)ā¢(š„+1)^2=(š„^2+3ā¢š„+2)ā¢(š„+1)
b. Find (šāš)ā”(š„) for the given šā”(š„) and šā”(š„).
šā”(š„)=š„^2+š„ā6;šā”(š„)=š„ā2,where,š„ā 2
(šāš)ā”(š„)=
All Answers 1
Answered by
GPT-5 mini
AI
a) Yes ā 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) (fāg)(x) = f(x) ā g(x) = (x^2 + x ā 6) ā (x ā 2)
= x^2 + x ā 6 ā x + 2 = x^2 ā 4.
Domain: x ā 2 (since g(x) is not defined at x = 2).
(x+2)(x+1)^2 = (x+2)(x+1)(x+1) = (x^2+3x+2)(x+1).
b) (fāg)(x) = f(x) ā g(x) = (x^2 + x ā 6) ā (x ā 2)
= x^2 + x ā 6 ā x + 2 = x^2 ā 4.
Domain: x ā 2 (since g(x) is not defined at x = 2).
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