Incorrect Your answer is incorrect. (f+g)(x) Your answer is incorrect. (fcdot g)(x) Your answer is incorrect. (f-g)(1) Your answer is incorrect. Suppose that the functions fand g are defined for all real numbers x as follows. f(x)=2x-6 g(x)=x-3 Write the expressions for (f+g)(x) and (fcdot g)(x) and evaluate (f-g)(1) (f+g)(x)= square (fcdot g)(x)= square (f-g)(1)= square

Let's go through each part step by step.<br /><br />### 1. Finding \((f+g)(x)\)<br /><br />Given:<br />\[ f(x) = 2x - 6 \]<br />\[ g(x) = x - 3 \]<br /><br />To find \((f+g)(x)\), we add the two functions:<br />\[ (f+g)(x) = f(x) + g(x) \]<br />\[ (f+g)(x) = (2x - 6) + (x - 3) \]<br />Combine like terms:<br />\[ (f+g)(x) = 2x + x - 6 - 3 \]<br />\[ (f+g)(x) = 3x - 9 \]<br /><br />So,<br />\[ (f+g)(x) = 3x - 9 \]<br /><br />### 2. Finding \((f \cdot g)(x)\)<br /><br />To find \((f \cdot g)(x)\), we multiply the two functions:<br />\[ (f \cdot g)(x) = f(x) \cdot g(x) \]<br />\[ (f \cdot g)(x) = (2x - 6) \cdot (x - 3) \]<br /><br />Use the distributive property to expand:<br />\[ (f \cdot g)(x) = 2x \cdot x + 2x \cdot (-3) - 6 \cdot x - 6 \cdot (-3) \]<br />\[ (f \cdot g)(x) = 2x^2 - 6x - 6x + 18 \]<br />Combine like terms:<br />\[ (f \cdot g)(x) = 2x^2 - 12x + 18 \]<br /><br />So,<br />\[ (f \cdot g)(x) = 2x^2 - 12x + 18 \]<br /><br />### 3. Evaluating \((f-g)(1)\)<br /><br />To find \((f-g)(x)\), we subtract the two functions:<br />\[ (f-g)(x) = f(x) - g(x) \]<br />\[ (f-g)(x) = (2x - 6) - (x - 3) \]<br />\[ (f-g)(x) = 2x - 6 - x + 3 \]<br />Combine like terms:<br />\[ (f-g)(x) = x - 3 \]<br /><br />Now, evaluate at \(x = 1\):<br />\[ (f-g)(1) = 1 - 3 \]<br />\[ (f-g)(1) = -2 \]<br /><br />So,<br />\[ (f-g)(1) = -2 \]<br /><br />### Summary<br /><br />\[<br />(f+g)(x) = 3x - 9<br />\]<br />\[<br />(f \cdot g)(x) = 2x^2 - 12x + 18<br />\]<br />\[<br />(f-g)(1) = -2<br />\]