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...

Frank Guyton

Frank Guyton

Answered

2021-12-28

Find two functions f(x) and g(x) so that h(x)=(fg)(x)
a) h(x)=(2x+3)2
b) h(x)=|32xx2|.
c) h(x)=h(x)=53x
d) h(x)=5{x3+4x2+1}

Answer & Explanation

Buck Henry

Buck Henry

Expert

2021-12-29Added 33 answers

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

kaluitagf

Expert

2021-12-30Added 38 answers

b)Here,
h(x)=|32xx2|
It is given that,
h(x)=fοg(x)
By comparing both equations,
fοg(x)f(x)×g(x)f(x)×g(x)Hence,
fog(x)=|32xx2|
f(x)×g(x)=|33x+xx2|
f(x)×g(x)=|(x+1)(x+3)|
Hence, f(x)=(1x) and g(x)=(x+3)
karton

karton

Expert

2022-01-09Added 439 answers

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

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