If #h(x)=(f+g)(x), f(x)=5x+2# how do you determine g(x) given #h(x)=x^2+5x+2#?

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Answer 1 · 2018-05-16T23:41:40

# g(x) = x^2 #

We have:

# h(x)=(f+g)(x), f(x)=5x+2#

and we seek #g(x)# given #h(x)=x^2+5x+2#

We can write

# h(x) = (f+g)(x) #
# \ \ \ \ \ \ \ = f(x)+g(x) #

So using #f(x)=5x+2# and #h(x)=x^2+5x+2#, then:

# h(x) = f(x)+g(x) => x^2+5x+2 = 5x+2 + g(x) #

So then:

# g(x) = (x^2+5x+2) - (5x+2) #
# \ \ \ \ \ \ \ = x^2+5x+2 - 5x-2 #
# \ \ \ \ \ \ \ = x^2 #