If g(x) = 2x +2 and fg(x) = 8x + 13, find f(x).
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Correct option is
B
x
2
+2
g(x)=1+
x
And f(g(x))=3+2
x
+x
then f(x)=?
f(g(x))=3+2
x
+x [ terms splitting]
f(g(x))=2+(1+2
x
+x)
Also, (1+
x
)
2
=1+x+2
x
⇒f(g(x))=2+(1+
x
)
2
⇒f(x)=2+x
2
f(x)=x
2
+2
checking
fog=(1+
x
)
2
+2 [(a+b)
2
=a
2
+b
2
+2ab]
=1+x+2
x
+2
=x+2
x
+3= given fog
⇒f(x)=
x
2
+2
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