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Let $f$ be the function $f: x \mapsto x^2 - 3x + 12$ - Junior Cycle Mathematics - Question 13 - 2013

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Question 13

Let-$f$-be-the-function-$f:-x-\mapsto-x^2---3x-+-12$-Junior Cycle Mathematics-Question 13-2013.png

Let $f$ be the function $f: x \mapsto x^2 - 3x + 12$. Let $g$ be the function $g: x \mapsto 2^{x-1}$. Show that $f(4) = g(5).$

Worked Solution & Example Answer:Let $f$ be the function $f: x \mapsto x^2 - 3x + 12$ - Junior Cycle Mathematics - Question 13 - 2013

Step 1

Calculate $f(4)$

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Answer

To find f(4)f(4), we substitute 4 into the function:

f(4)=(4)2−3(4)+12f(4) = (4)^2 - 3(4) + 12

Calculating each term, we have:

  1. (4)2=16(4)^2 = 16
  2. −3(4)=−12-3(4) = -12
  3. Combining these,

f(4)=16−12+12=16.f(4) = 16 - 12 + 12 = 16.

Step 2

Calculate $g(5)$

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Answer

Next, we find g(5)g(5) by substituting 5 into the function:

g(5)=25−1=24.g(5) = 2^{5-1} = 2^{4}.

Calculating this, we have:

g(5)=16.g(5) = 16.

Step 3

Show that $f(4) = g(5)$

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Answer

From our calculations, we observed:

  • f(4)=16f(4) = 16
  • g(5)=16g(5) = 16

Thus, we conclude that: f(4)=g(5)=16.f(4) = g(5) = 16.

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