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Find the value of π given π of π₯ equals ππ₯ plus 13 and π of eight is equal to negative 11.
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Here is our function.
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π is sort of the name of the function.
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And π₯ is what goes in; itβs its input.
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Weβve also been given some information about the value of π of eight.
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In other words, our input is no longer π₯.
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Itβs eight.
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And when the input is eight, the output is negative 11.
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So, letβs see what happens when we put eight into our definition of the function here.
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π of eight means each time we see the π₯, we replace or substitute it with eight.
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So, π of eight becomes π times eight plus 13.
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Letβs write that as eight π plus 13.
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But of course, we know that π of eight is equal to negative 11.
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So, this must mean that eight π plus 13 must be equal to negative 11.
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And so, our job, weβre trying find the value of π, is to solve this equation.
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Weβll do this by performing a series of inverse operations.
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The first thing weβre going to do is subtract 13 from both sides of our equation.
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Remember, eight π plus 13 minus 13 is just eight π.
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And negative 11 minus 13 means we move 13 spaces further down the number line.
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And we get to negative 24.
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So, eight π is equal to negative 24.
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The eight is multiplying the π.
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And so, the inverse operation we apply next is to divide both sides of our equation by eight.
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That leaves π on the left-hand side.
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And since 24 divided by eight is three, we know negative 24 divided by eight is negative three.
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And so, given π of π₯ is equal to ππ₯ plus 13 and π of eight is equal to negative 11, we find π is equal to negative three.
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Now, we can check our answer by letting π of π₯ now be equal to negative three π₯ plus 13.
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Weβve replaced π with negative three.
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Weβre going to check that the value of π of eight is indeed negative 11.
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And so, we replace π₯ with eight.
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And we get negative three times eight plus 13.
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Thatβs negative 24 plus 13, which is negative 11 as required.