Evaluating Functions?

[wrongnmbr]

Can someone confirm whether or not I've done these correctly?

1. Find (f + g)(x)
f(x) = -6x^2 - 2x - 7
g(x) = -8x^2 - 2x - 5
MY ANSWER: -14x^2 - 4x - 12

2. Evaluate the following function for f(x) = -3x^2 + 6 and g(x) = 8x + 2
(f + g)(4)
MY ANSWER: -12x^2 + 32x + 32

3. Evaluate the indicated function for f(x) = x^2 - 8 and g(x) = x + 9
(fg)(-2)
MY ANSWER: 2x^3 + 8x^2 - 16x - 144

 

[BigGlenntheHeavy]

\(\displaystyle By \ definition, \ (f+g)(x) \ = \ f(x)+g(x) \ and \ (fg)(x) \ = \ f(x)g(x).\)

\(\displaystyle What's \ wrong \ with \ answers \ 2 \ and \ 3?\)

 

[wrongnmbr]

I don't understand. For #2 I added f(x) and g(x) then multiplied by 4, as it directed. And for #3, I multiplied f(x) and g(x) then multiplied by -2 (although the signs should be changed). What am I doing wrong...?

 

[mmm4444bot]

What am I doing wrong ?

You misunderstand function notation.

The symbol f(x) does not mean f times x.

Likewise, the symbol f(4) does not mean f times 4.

And the symbol (f+g)(4) does not mean (f+g) times 4.

The symbol (f+g)(4) represents a single number.

It is the number you get when x = 4 in the expression f + g.

 

[mmm4444bot]

1. Find (f + g)(x)
f(x) = -6x^2 - 2x - 7
g(x) = -8x^2 - 2x - 5
MY ANSWER: -14x^2 - 4x - 12 ? This is correct

Now, FOR EXAMPLE, if you wanted to evaluate (f+g)(2), then you substitute x = 2 into (f+g)(x)

(f+g)(2) = -14(2)^2 - 4(2) - 12, and simplify.

We see that (f+g)(2) = -212

 

[BigGlenntheHeavy]

\(\displaystyle 2) \ f(x) \ = \ -3x^2+6 \ and \ g(x) \ = \ 8x+2.\)

\(\displaystyle (f+g)(x) \ = \ -3x^2+8x+8, \ (f+g)(4) \ = \ -3(4)^2+(8)(4)+8 \ = -48+32+8 \ = \ -8 \ or\)

\(\displaystyle f(4) \ = \ -3(4)^2+6 \ = \ -42 \ and \ g(4) \ = \ (8)(4)+2 \ = \ 34, \ hence\)

\(\displaystyle (f+g)(4) \ = \ f(4)+g(4) \ = \ -42+34 \ = \ -8\)

\(\displaystyle Got \ It.\)