1.-/2 pointsTGInterAlgHS 9.1.E01ab. EXAMPLE 1 . 2x2 + 1 and g(x) = 5x-3. Find ea

Question

1.-/2 pointsTGInterAlgHS 9.1.E01ab. EXAMPLE 1 . 2x2 + 1 and g(x) = 5x-3. Find each function and its domain. (a) f+g (b) f-g Let Strategy We will add and subtract the functions as if they were binomials. Why We add because of the plus symbol in f+g, and we subtract because of the minus symbol in f-g Solution (a) (f+ g)x)-x)+g(x) (2x2+1)+ (5x - 3) Replace fx) with 2x2 + 1 and g(x) with 5x-3. - 2x2 +1+ 5x-3 Drop the parentheses. 2x2 + 5x-2 Combine like terms. The domain of f+ g is the set of real numbers that are in the domain of both f and g. Since the domain of both fand g is the interval (,), the domain of f+g is also the interval -,o). (b)x)-x)-gtx) - (2x2 +1)-(5x -3) -2x2 +1-5x +3 2x2 -5x +4 Combine like terms. Change the sign of each term of 5x-3 and drop the parentheses Since the domain of both f and g is (-, e), the domain of f - g is also the interval (, 0) Self Check Let x)5x2+1 and gx)-5x-6. Find

Explanation / Answer

f(x) = 5x^2 + 1

g(X) = 5x - 6

a) ( f+ g)(x) = f(x) + g(x)

= 5x^2 + 1 + 5x - 6

= 5x^2 + 5x - 5

b) ( f - g)(x) = f(x) - g(x)

= 5x^2 +1 - ( 5x - 6)

= 5x^2 + 1 - 5x + 6

= 5x^2 - 5x + 7

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