How do you find (f-g)(3) given f(x)=x^2-1 and g(x)=2x-3 and h(x)=1-4x#?

1 Answer
Douglas K.
Apr 3, 2017

Compute (f-g)(x) and then evaluate at x = 3

OR

Evaluate f(3)" and "g(3) and then perform the subtraction.

(f-g)(3) = f(3)-g(3)

Explanation:

Compute (f-g)(x):

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

Substitute the equivalents for f(x)" and " g(x)

(f-g)(x) = x^2-1 - (2x-3)

Distribute the minus sign:

(f-g)(x) = x^2-1 -2x+3

Combine like terms:

(f-g)(x) = x^2 -2x+2

Evaluate at x = 3:

(f-g)(3) = 3^2 -2(3)+2

(f-g)(3) = 5

OR

Evaluate f(x)" at "x=3:

f(3) = 3^2 - 1#

f(3) = 8

Evaluate g(x)" at "x=3

g(3) = 2(3)-3

g(3) = 3

(f-g)(3) = f(3)-g(3)

(f-g)(3) = 8-3

(f-g)(3) = 5

Either always works.

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