Find (f+g)(x) for f(x)=1/2x+4 and g(x)=x-3?
We need to determine the sum of the two functions `f(x) = 1/2 x +4 ` and `g(x) = x-3` . So we have
`(f+g)(x) = f(x) + g(x)`
`=1/2 x +4 + (x-3)`
Remove the parentheses around the expression `x-3.`
`=1/2 x +4 + x-3`
Subtract `3 ` from `4 ` to get ` 1.`
`=1/2x +x +1`
To add fractions, the denominators must be equal. The denominators can be made equal by finding the least common denominator (LCD). In this case, the LCD is 2. Next, multiply each fraction by a factor of 1 that will create the LCD in each of the fractions.
`=1/2x + x*2/2 +1`
Multiply x by 2 to get 2x.
`=1/2x + (2x)/2 +1`
Combine the numerators of all expressions that have common denominators.
According to the distributive property, for any numbers a, b, and c, a(b+c)=ab+ac and (b+c)a=ba+ca. Here, x is a factor of both x and 2x.
Add 2 to 1 to get 3.
`=3x/2 + 1`
Find `(f + g)(x).`
`(f + g)(x) = f(x) + g(x)` .
`(f + g)(x) = (1/2x+ 4) + (x - 3).`
`(f + g)(x) =` `3/2x + 1`
The solution is: `(f + g)(x) = 3/2x + 1`