Find two functions f(x) and g(x) so that h(x)=(f∘g)(x) a) h(x)=(2x+3)2 b) h(x)=|3−2x−x2|. c) h(x)=h(x)=53−x d) h(x)=5{x3+4x2+1}

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Find two functions f(x) and g(x) so that h(x)=(f∘g)(x)  a) h(x)=(2x+3)2  b) h(x)=|3−2x−x2|.   c) h(x)=h(x)=53−x  d) h(x)=5{x3+4x2+1}

Buck Henry · Accepted Answer

Given data,  The function h(x) is defined as h(x)=fοg(x)  Step 1  a)Here,  h(x)=(2x+3)2  It is given that,  h(x)=fοg(x)  By comparing both equations,  fοg (x)=(2x+3)2  f(x)×g(x)=(2x+3)×(2x+3)

kaluitagf · Accepted Answer

b)Here,  h(x)=|3−2x−x2|  It is given that,  οh(x)=fοg(x)  By comparing both equations,  fοg(x)f(x)×g(x)f(x)×g(x)Hence,  fog(x)=|3−2x−x2|  f(x)×g(x)=|3−3x+x−x2|  f(x)×g(x)=|(−x+1)(x+3)|  Hence, f(x)=(1−x) and g(x)=(x+3)

karton · Accepted Answer

Step 2 c)Here, h(x)=53−x It is given that, οh(x)=fοg(x) By comparing both equations, fog=53−x f(x)×g(x)=5×13−x Hence, f(x)=5 and g(x)=13−x Step 3 d)Here, f(x)=x3+4x2+15 It is given that, οh(x)=fοg(x) By comparing both equations, fog(x)=x3+4x2+15 f(x)×g(x)=x3+4x2+12×x3+4x2+13 Hence, f(x)=x3+4x2+12 and g(x)=x3+4x2+13

Find two functions f(x) and g(x) so that h(x) =

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