Suppose that g (x) = 1 + 1x and f(g(x)] = 3 + 2x + x, then f (x)
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Step-by-step explanation:
Answer
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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