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QUESTION: For f(x)=x+3 and g(x) =2x+5, find the following

a. (fog)(x)=

b. (gof)(x)=

c. (fog)(-1)=

ANSWER: What I believe that symbol is the same as is (fog)(x) = f(g(x)).

Is that correct?

This means we have

a. f(g(x)) = g(x) + 3, so it is 2x + 5 + 3 = 2x + 8.

b. g(f(x)) = 2*f(x) + 5 = 2(x+3) + 5 = 2x + 6 + 5 = 2x + 11.

c. f(g(-1) = f(2(-1)+5) = f(-2+5) = f(3) = 3+3 = 6.

---------- FOLLOW-UP ----------

QUESTION: Evaluate the function at the given values of the independent variable and simplify.

f(x)=4xsquare2-1/x2

a. f(3)

b. f(-3)

c. f(-x)

If that suppose to be 4x²-1/x²?

That is, are both x's squared?

a. Put in 3 as x and get 4*9 - 1/9 = 323 8/9.

b. Put in -3 as x and get the same thing, since when squared the -3 still gives a 9.

c. When putting in a negative the answer is the equation 4x²-1/x² since a negative squared is still positive. That is, x² = (-x)².

Algebra

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