If we define the functions f, g and h that map R into R by :
If we define the functions f, g and h that map R into R by :
f(x) = x⁴, g(x) = √(x² + 1), h(x) = x² + 72, then the value of the composite functions ho(gof) and (hog)of are given as
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Correct answer: (D) x⁸ + 73 and x⁸ + 73
Explanation
gof(x) = √(x⁸ + 1), so ho(gof)(x) = (x⁸ + 1) + 72 = x⁸ + 73. hog(x) = (x² + 1) + 72 = x² + 73, so (hog)of(x) = x⁸ + 73. Hence both are x⁸ + 73.