For what value of x is fog=gof if f(x)=x−2 and g(x)=x3+3?
A
−23
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B
−1
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C
32
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D
−32
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Solution
The correct option is B−1 f(x)=x−2g(x)=x3+3f[g(x)]=g(x)−2⇒fog=x3+3−2=x3+1g[f(x)]={f(x)}3+3⇒gof=(x−2)3+3fog=gofx3+1=(x−2)3+3x3−2=(x−2)3x3−2=x3−8−6x(x−2)x3−2=x3−8−6x2+12x⇒x2+1+2x=0⇒(x+1)2=0⇒x=−1