Questions: Given the following functions, find each of the values: f(x)=x^2-5x+6 g(x)=x-2 (f+g)(-2)=16 (f-g)(-5)=63 (f * g)(4)=4 (f/g)(-3)=1

Transcript text: Cengage Learning Course Modules: MATH140 wamap.org/assess2/?cid=39721\&aid=2279530\#/skip/1 HW Algebra \& Composition of Functions Score: 1.5/30 Answered: 1/17 Question 1 Score on last try: 1.5 of $\mathbf{2 ~ p t s . ~ S e e ~ D e t a i l s ~ f o r ~ m o r e . ~}$ Next question Get a similar question You can retry this question Given the following functions, find each of the values: \[ \begin{array}{l} f(x)=x^{2}-5 x+6 \\ g(x)=x-2 \\ (f+g)(-2)=16 \\ (f-g)(-5)=63 \\ (f \cdot g)(4)=4 \\ \left(\frac{f}{g}\right)(-3)=1 \end{array} \] Question Help: Video D Post to forum Submit Question Jump to Answer esc 80 F3 F4

Solution

Solution Steps

Step 1: Calculate $ (f+g)(-2) $

We start by evaluating the expression $ (f+g)(-2) $. The functions are defined as follows: \[ f(x) = x^2 - 5x + 6 \] \[ g(x) = x - 2 \] Thus, we have: \[ f + g = (x^2 - 5x + 6) + (x - 2) = x^2 - 4x + 4 \] Now, substituting $ x = -2 $: \[ (f+g)(-2) = (-2)^2 - 4(-2) + 4 = 4 + 8 + 4 = 16 \]

Step 2: Calculate $ (f-g)(-5) $

Next, we evaluate $ (f-g)(-5) $: \[ f - g = (x^2 - 5x + 6) - (x - 2) = x^2 - 6x + 8 \] Now, substituting $ x = -5 $: \[ (f-g)(-5) = (-5)^2 - 6(-5) + 8 = 25 + 30 + 8 = 63 \]

Step 3: Calculate $ (f \cdot g)(4) $

Now, we evaluate $ (f \cdot g)(4) $: \[ f \cdot g = (x^2 - 5x + 6)(x - 2) \] To find $ (f \cdot g)(4) $, we substitute $ x = 4 $: \[ f(4) = 4^2 - 5(4) + 6 = 16 - 20 + 6 = 2 \] \[ g(4) = 4 - 2 = 2 \] Thus, \[ (f \cdot g)(4) = f(4) \cdot g(4) = 2 \cdot 2 = 4 \]