Question 824541: Decide whether the composite functions of fog and gof, are equal to x.
f(x)=x^3 + 7, g(x)= cube root(x-7)
Answers:
A) Yes, no
B) No, yes
C) No, no
D) Yes, yes
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Decide whether the composite functions of fog and gof, are equal to x.
f(x)=x^3 + 7, g(x)= cube root(x-7)
fog(x) = f[g(x)] = f[cbrt(x-7)] = (cbrt(x-7)^3+7 = x-7+7 = x
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gof(x) = g[f(x)] = g[x^3+7] = cbrt[x^3+7-7] = cbrt(x^3) = x
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Answers:
A) Yes, no
B) No, yes
C) No, no
D) Yes, yes
Answer: D
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Cheers,
Stan H.
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