Use the inner product〈f, g〉=∫10f(x)g(x)dxin the vector space c0[0,1] of continuous functions on the domain [0,1] to find 〈f, g〉, ∥f∥, ∥g∥, and the angle αf, g between f(x) and g(x) forf(x)=−10x2−6 and g(x)=−9x−4.〈f, g〉= ,∥f∥= ,∥g∥= ,αf, g .

a) <f,g> = 2605/3

b) ∥f∥ = 960

c) ∥g∥ = 790

d) α = 90  

Explanation

a) We calculate  <f,g> using the definition of the inner product:

b) How

∥f∥ = <f,f> then:

∥f∥ =

c)

∥g∥ = <g,g>

∥g∥ =

d) Angle between f and g

<f,g> = ∥f∥∥g∥cosα

Thus

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step-by-step explanation: