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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\# $?

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Last updated date: 22nd Feb 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 $(f - g)(3)$.

Complete step by step answer:
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 $g(x)$.
$(f - g)(x) = {x^2} - 1 - (2x - 3)$
Now we will open the brackets.
$(f - g)(x) = {x^2} - 1 - 2x + 3$
Now we will combine all the like terms.
$(f - g)(x) = {x^2} - 2x + 2$
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 $5$.

Note:While substituting the terms make sure you are taking into account the signs of the terms as well. While opening the brackets open with their respective signs and remember to multiply the signs as well.A function notation is the way of writing a function. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation. Traditionally, functions are referred to by single letter names. To evaluate function, substitute the input given number or expression or expression for the function’s variable. Finally calculate the result.