Given #f(x)=4x-1# and #g(x)=x+6#, what is #(f+g)(x)#?

1 Answer
JSA
Mar 5, 2018

#(f+g)(x)# is the same as #f(x) + g(x)#

Explanation:

Since #(f+g)(x)# is the same as #f(x) + g(x)#, you take what #f(x)# is equal to, which in this case is #4x-1# and you add that to #g(x)#, which is #x+6#.

Make sure to use brackets just in case the sign changes due to an equation like #(f-g)(x)#:

#(4x-1) + (x+6) = ?#

Remove the brackets:

#4x-1+x+6 = ?#

Combine like terms:

#4x + x = 5x# and #-1+6 = 5#

You're left with #5x + 5# and that may seem like the answer, but you can still factor a 5 out:

#5x+5 = 5(x+1)#

Therefore, #(f+g)(x) = 5(x+1)#

I hope that clarified it for you.

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