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Worked solution

Substitute a complete input expression

The function ff is defined by f:x↦3x2+1f:x\mapsto3x^2+1, x∈Rx\in\mathbb R. Find (a) f(3)f(3), (b) f(5x)f(5x), (c) f(2y+1)f(2y+1).

CJC · Functions · Example 1

(a) Evaluate at 3

Answer

f(3)=28f(3)=28.

The Teacher completes the Student blank: f(3)=3(3)2+1=28f(3)=3(3)^2+1=28.

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(b) Substitute 5x

Answer

f(5x)=75x2+1f(5x)=75x^2+1.

Replace the entire input by 5x5x: f(5x)=3(5x)2+1=75x2+1f(5x)=3(5x)^2+1=75x^2+1. Squaring affects the factor 5 as well as x.

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(c) Substitute 2y+1

Answer

f(2y+1)=12y2+12y+4f(2y+1)=12y^2+12y+4.

The printed stages are 3(2y+1)2+1=3(4y2+4y+1)+1=12y2+12y+43(2y+1)^2+1=3(4y^2+4y+1)+1=12y^2+12y+4. Keep the whole input in parentheses before expanding.

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