Let ϕ(x)=8, ψ(x)=-2x+9, and χ(x)=6x². Consider the inner product ⟨ f, g ⟩ = ∫₀⁴ ϕ(x)ψ(x)χ(x)dx in the vector space V₀[0,4] of continuous functions on the domain [0,4] . Use the Gram-Schmidt process to determine an orthonormal basis for the subspace of V₀[0,4] spanned by the functions ϕ(x), ψ(x), and χ(x).
a) 1/√210ϕ(x), 1/√210ψ(x), 1/√210χ(x)
b) 1/√98ϕ(x), 1/√98ψ(x), 1/√98χ(x)
c) 1/√15ϕ(x), 1/√15ψ(x), 1/√15χ(x)
d) 1/√45ϕ(x), 1/√45ψ(x), 1/√45χ(x)
