QuestionFind $(f-g)(4)$ where $f(x)=4x-3$ and $g(x)=x^3+2x$ .

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x) =4x -3$ . The function $g(x)$ is given by $g(x) = x^3 +x$
3. We are asked to find the value of $(f - g)(4)$ , which means we need to subtract the value of function $g$ at $x =4$ from the value of function $f$ at $x =4$

STEP 2

First, we need to find the value of $f(4)$ . We can do this by substituting $x =4$ into the function $f(x)$ .
$f(4) =4(4) -$

STEP 3

Now, calculate the value of $f()$ .
$f() =() -3 =16 -3 =13$

STEP 4

Next, we need to find the value of $g(4)$ . We can do this by substituting $x =4$ into the function $g(x)$ .
$g(4) = (4)^3 +2(4)$

STEP 5

Now, calculate the value of $g(4)$ .
$g(4) = (4)^3 +2(4) =64 +8 =72$

STEP 6

Now that we have the values of $f(4)$ and $g(4)$ , we can find the value of $(f - g)(4)$ by subtracting the value of $g(4)$ from the value of $f(4)$ .
$(f - g)(4) = f(4) - g(4)$

STEP 7

Plug in the values for $f(4)$ and $g(4)$ to calculate $(f - g)(4)$ .
$(f - g)(4) =13 -72$

STEP 8

Calculate the value of $(f - g)(4)$ .
$(f - g)(4) =13 -72 = -59$ So, $(f - g)(4) = -59$ .

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