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Question

Find the point of discontinuity of y=f(u), where f(u)=32u2+5u3 and u=1x+2

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Solution

u=1x+2 for u to be real value
x+20or,x2
f(u)=32u2+5u3=321(x+2)2+5x+23=3(x+2)22+5(x+2)3(x+2)2
reducing denominator:
3[x2+4x+4]+5x+10+2=3x212x12+5x+10+2=3x27xf(x)=3(x+2)23x27x=3(x+2)2x[3x+7]
for f(u) to be defined
x03x+70x73at,x=2,0,73
funtion is discontinuous as it is undefined at those points.

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