Q. 1 C

# Find gof and fog when f: R → R and g: R → R is defined byf(x) = x2 + 8 and g(x) = 3x3 + 1

Since, f:R R and g:R R

fog:R R and gof:R R

f(x)=x2 + 8 and g(x)=3x3 + 1

So, gof(x)= g(f(x))

gof(x)= g(x2 + 8)

gof(x)= 3(x2 + 8)3 + 1

gof(x)= 3(x6 + 512 + 24x4 + 192x2) + 1

gof(x)= 3x6 + 72x4 + 576x2 + 1537

Similarly, fog(x)=f(g(x))

fog(x)= f(3x3 + 1)

fog(x)=(3x3 + 1)2 + 8

fog(x)=(9x6 + 1 + 6x3) + 8

fog(x)=9x6 + 6x3 + 9

So, gof(x) = 3x6 + 72x4 + 576x2 + 1537 and fog(x) = 9x6 + 6x3 + 9

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