Given the function f(x)=8x-2 and g(x)=-6x+13  find the following: a. (f-g)(x)=     b. (f-g)(3)=    c. (f*g)(x)=     d. (f*g)(0)=

Let's go step by step to solve the given problems based on the functions \( f(x) = 8x - 2 \) and \( g(x) = -6x + 13 \).

### a. \((f - g)(x)\)
\[
(f - g)(x) = f(x) - g(x)
\]
Substitute the given expressions for \( f(x) \) and \( g(x) \):
\[
(f - g)(x) = (8x - 2) - (-6x + 13)
\]
Simplify the expression:
\[
(f - g)(x) = 8x - 2 + 6x - 13 = (8x + 6x) + (-2 - 13) = 14x - 15
\]
So, 
\[
(f - g)(x) = 14x - 15
\]

### b. \((f - g)(3)\)
Substitute \( x = 3 \) into \((f - g)(x) = 14x - 15\):
\[
(f - g)(3) = 14(3) - 15 = 42 - 15 = 27
\]
So, 
\[
(f - g)(3) = 27
\]

### c. \((f \cdot g)(x)\)
\[
(f \cdot g)(x) = f(x) \cdot g(x)
\]
Substitute the given expressions for \( f(x) \) and \( g(x) \):
\[
(f \cdot g)(x) = (8x - 2) \cdot (-6x + 13)
\]
Use the distributive property to multiply:
\[
(f \cdot g)(x) = 8x \cdot (-6x) + 8x \cdot 13 - 2 \cdot (-6x) - 2 \cdot 13
\]
Simplify:
\[
(f \cdot g)(x) = -48x^2 + 104x + 12x - 26 = -48x^2 + 116x - 26
\]
So, 
\[
(f \cdot g)(x) = -48x^2 + 116x - 26
\]

### d. \((f \cdot g)(0)\)
Substitute \( x = 0 \) into \((f \cdot g)(x) = -48x^2 + 116x - 26\):
\[
(f \cdot g)(0) = -48(0)^2 + 116(0) - 26 = -26
\]
So, 
\[
(f \cdot g)(0) = -26
\]

### Summary of the answers:
a. \((f - g)(x) = 14x - 15\)  
b. \((f - g)(3) = 27\)  
c. \((f \cdot g)(x) = -48x^2 + 116x - 26\)  
d. \((f \cdot g)(0) = -26\)

Would you like more details on any of these steps, or do you have any other questions?

Here are 5 related questions for further practice:
1. Find \((f + g)(x)\) for the same functions \(f(x)\) and \(g(x)\).
2. Compute \((f + g)(2)\).
3. Find the derivative of \((f \cdot g)(x)\).
4. Determine the x-value where \((f - g)(x) = 0\).
5. Find the x-intercepts of \((f \cdot g)(x)\).

**Tip:** When combining functions, always distribute and combine like terms carefully to avoid errors in signs and coefficients.

Given the function f(x)=8x-2 and g(x)=-6x+13, find the following: a. (f-g)(x)= b. (f-g)(3)= c. (f*g)(x)= d. (f*g)(0)=

Learn how to perform function operations with detailed solutions for (f-g)(x) and (f*g)(x) given f(x)=8x-2 and g(x)=-6x+13. Includes step-by-step solutions for subtracting and multiplying functions, along with evaluating them at specific values like x=3 and x=0. Suitable for Grades 9-10.

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