Given $f (x) = x^{2} - 4$ $f(x) = x^2 - 4$ and g(x) = 2x - 1 , how do you determine the value of (f + g)(3)?

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Answer 1 · 2017-04-14T14:06:48

See the entire solution process below:

$(f + g) (x) = f (x) + g (x) = (x^{2} - 4) + (2 x - 1)$ $(f + g)(x) = f(x) + g(x) = (x^2 - 4) + (2x - 1)$

Therefore:

$(f + g) (x) = (x^{2} - 4) + (2 x - 1)$ $(f + g)(x) = (x^2 - 4) + (2x - 1)$

To find $(f + g) (3)$ $(f + g)(3)$ we must substitute $3$ $color(red)(3)$ for every occurrence of $x$ $color(red)(x)$ in $(f + g) (x)$ $(f + g)(x)$ :

$(f + g) (x) = (x^{2} - 4) + (2 x - 1)$ $(f + g)(color(red)(x)) = (color(red)(x)^2 - 4) + (2color(red)(x) - 1)$ becomes:

$(f + g) (3) = (3^{2} - 4) + ((2 \cdot 3) - 1)$ $(f + g)(color(red)(3)) = (color(red)(3)^2 - 4) + ((2 * color(red)(3)) - 1)$

$(f + g) (3) = (9 - 4) + (6 - 1)$ $(f + g)(color(red)(3)) = (9 - 4) + (6 - 1)$

$(f + g) (3) = 5 + 5$ $(f + g)(color(red)(3)) = 5 + 5$

$(f + g) (3) = 10$ $(f + g)(color(red)(3)) = 10$

Given f(x)=x2−4f(x) = x^2 - 4 and g(x) = 2x - 1 , how do you determine the value of (f + g)(3)?