Functions: Transformations and Properties

Given f(x)= 2x−3 and g(x) = x2 − 4x + 5. Evaluate 2g(f(a- 1)) in simplest form

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Best answer

f(x)=2x-3, so f(a-1)=2(a-1)-3=2a-5.

g(x)=x2-4x+5, so g(2a-5)=(2a-5)2-4(2a-5)+5=

4a2-20a+25-8a+20+5=4a2-28a+50.

Therefore, g(f(a-1))=4a2-28a+50.

QUICK CHECK

Let a=2, then f(a-1)=f(1)=-1; g(-1)=10.

4a2-28a+50=16-56+50=10=g(f(2-1)) OK

by Top Rated User (1.2m points)

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