Given the inner product space of polynomials with real coefficients, degree ≤n_(P₁(R),+,,°), where, Pn = {p(x)=anx +...+a₁x +ão | a¡¤R, İ= {0, 1,...,n}}, 。 : PnxPn →R+ : (p(x), q(x)) → p(x) q(x) = f(x)q(x) dx and the subset S={p₁(x)=1, p₂2(x)=x, P³(x)=2x²+x+1} of Pn. Find an orthonormal basis of the vector subspace W=span(p₁(x),p2(x),p³(x)).

Q: Show that f(x) = (3x + 2)/(5x-1) is invertible. Determine the domain and range of f and f-1.

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Q: The zeros for Ax) = x-4x-9x + 36x are 1) (0,+3,4) 2) (0,3,4) 3) (0,±3,-4) 4) (0,3,-4)

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Q: P(x1, #2) –X2, Q(x1, x2) = x1; D = {(x1,x2) :0 < x1 < 1,0 < x2 < 1}. = -

A: Note : " As per our guidelines we will solve only first question . If you want any specific question…

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A: The solution is given below.