Veritas Algebra Lesson Book Question 91 explanation

Question

91. If g is a function defined for all x by g(2x) = (x^4)/ 16, then what is the value of g(2x) in terms of g(x)?

I'm not sure where to go with this one. Any help?

Thanks

KarishmaB · Answer

Before I answer this one, let me ask you one question.

If f(x) = 24x + 5
what is f(2x)?
What do you do? You put 2x in place of x everywhere and proceed.
So
f(2x) = 24(2x) + 5

In this question, g(2x) is defined for you. You need g(x)
g(2x) = x^4/16

You need g(x) so in place of 2x you substitute x everywhere. 
First, bring in a 2x.

g(2x) = \frac{x^4}{16} = \frac{16*x^4}{16*16} = \frac{(2x)^4}{16*16}

Now replace 2x by x.
 g(x) = \frac{x^4}{16*16}

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