Let lower f left-parenthesis x right-parenthesis equals Start Fraction 4 x minus 3 over x minus 10 End Fraction and lower g left-parenthesis x right-parenthesis equals Start Fraction 2 x minus 8 over x minus 10 End Fraction. Find left-parenthesis f plus g right-parenthesis left-parenthesis x right-parenthesis. Assume all appropriate restrictions to the domain.
(1 point)
Responses
left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 6 x minus 11 over x minus 10 End Fraction
Image with alt text: left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 6 x minus 11 over x minus 10 End Fraction
left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 2 x plus 5 over x minus 10 End Fraction
Image with alt text: left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 2 x plus 5 over x minus 10 End Fraction
left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 6 x plus 11 over x minus 10 End Fraction
Image with alt text: left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 6 x plus 11 over x minus 10 End Fraction
left-parenthesis lower f plus lower g right-parenthesis left-parenthesis x right-parenthesis equals Start Fraction 6 x minus 11 over 2 x minus 20 End Fraction
The correct response is:
(left-parenthesis f plus g right-parenthesis left-parenthesis x right-parenthesis) equals (Start Fraction 6 x minus 11 over x minus 10 End Fraction)
To find f + g, we need to add the two given functions f(x) and g(x) together.
f(x) = (4x - 3)/(x - 10)
g(x) = (2x - 8)/(x - 10)
To add these two functions, we need to find a common denominator for the fractions. Since the denominators are the same, we can simply add the numerators together.
f(x) + g(x) = ((4x - 3)/(x - 10)) + ((2x - 8)/(x - 10))
Combining the fractions, we have:
= (4x - 3 + 2x - 8)/(x - 10)
= (6x - 11)/(x - 10)
Therefore, (f + g)(x) = (6x - 11)/(x - 10)