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# How do you find $(f - g)(3)$ given $f(x) = {x^{2 - 1}}$ and $g(x) = 2x - 3$ and $h(x) = 1 - 4x\#$?

Last updated date: 18th Jun 2024
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Hint:Start by computing the values for $(f - g)(x)$. Then one by one substitute the values of the terms $f(x)$ and $g(x)$. Then further open the brackets and combine all the like together. Finally evaluate the value of the function $(f - g)(3)$.

First we will start off by computing $(f - g)(x)$ and then evaluate the value of $x$ at $x = 3$.
$(f - g)(x) = f(x) - g(x)$
Now we will substitute the equivalents for $f(x)$ and $g(x)$.
$(f - g)(x) = {x^2} - 1 - (2x - 3)$
$(f - g)(x) = {x^2} - 1 - 2x + 3$
$(f - g)(x) = {x^2} - 2x + 2$
Now finally we will evaluate the value of $x$ at $x = 3$.
$(f - g)(x) = {x^2} - 2x + 2 \\ \Rightarrow(f - g)(3) = {3^2} - 2(3) + 2 \\ \Rightarrow (f - g)(x) = 9 - 6 + 2 \\ \therefore (f - g)(x) = 5 \\$
Hence, the value of the function $(f - g)(3)$ is $5$.