If f(x) = x 2 + 1 and g(x) = 3x + 1, find 2·f(4).

Question

I have narrowed it down to either 18, 34, or 65. I can not determine which one though.

Answer 1

f(4) = 4² + 1 = 17, so 2f(4) = 2(17) = 34.

Answer 2

Here is another answer which yields an interesting result.

 

Given f(x) = x²+1 and g(x) = 3x+1 we can use the 2nd equation to solve for x in terms of g(x), or, x = (g(x)-1)/3.

 

Let's put that in the f(x) equation and see what we get: f(x) = ((g(x) - 1)/3)² + 1. If we let x=4 then this reduces to 

((13-1)/3)²+1 = 17 and then multiply by 2 to get 34. You get the same answer.

 

Bob

Answer 3

I don't think your question is printing quite right. I'm interpreting it as:

f(x) = x^2 + 1

g(x) has no apparent use in this, but it is g(x) = 3 * x + 1. It is given to throw you off and make you doubt yourself, standardized test writers are jerks like that.

Finding 2*f(4) involves plugging the number 4 into f(x) as if it were x:

f(4) = 4^2 + 1
f(4) = 16 + 1
f(4) = 17

Now we can multiply that result by 2:

2 * f(4) = 2 * 17 = 34

Edited: WyzAnt, in all their glorious wisdom, blessings be upon them, saw fit to copy StackExchange's platform without implementing any of the features that would permit me to make this answer beautiful (Markdown and MathJaX). So, I'll make it look like garbage instead. Thanks WyzAnt for an inferior platform.

While I'm here on my soapbox (manually inserting linebreaks) I want to also note that stripping the StackExchange platform of its voting capabilities is completely wrongheaded. Implement the voting, and reputation tracking and let us tutors have something for our effort!!