For what values of x, f(x)=g(x), where f(x)=log, (2x² – 5x +11) and g(x) = 2.
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Answer:
f(x)=x−2
g(x)=x
3
+3
f[g(x)]=g(x)−2
⇒fog=x
3
+3−2=x
3
+1
g[f(x)]={f(x)}
3
+3
⇒gof=(x−2)
3
+3
fog=gof
x
3
+1=(x−2)
3
+3
x
3
−2=(x−2)
3
x
3
−2=x
3
−8−6x(x−2)
x
3
−2=x
3
−8−6x
2
+12x
⇒x
2
+1+2x=0
⇒(x+1)
2
=0
⇒x=−1
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