Question

Find f(x) and g(x) so the function can be expressed as y = f(g(x)).
y = Seven divided by x squared. + 10

this is a writing portion

Answer 1

@TheSmartOne

@pooja195

Answer 2

please help me. This is my last question..

Answer 3

\[\large\rm y=\frac{7}{x^2}+10\]

Answer 4

What if I gave you this function?\[\large\rm y=\frac{7}{~~~}+10\]Hmm what's missing?

Answer 5

x squared

Answer 6

So maybe we can call this f,\[\large\rm f=\frac{7}{~~~}+10\]And then we can stuff g inside of it,\[\large\rm f(g)=\frac{7}{g}+10\]

Answer 7

And you already know what your g should be at this point, yes?

Answer 8

x squared?

Answer 9

Yes good.\[\large\rm g=x^2\]

Answer 10

Lemme be a little more clear with f though,
we can't just leave a blank space in the function.
That's actually the x in the function.\[\large\rm f=\frac{7}{x}+10\]

Answer 11

The x is what gets replaced when we take a composition.

Answer 12

\[\large\rm f(g)=\frac{7}{g}+10\]bam\[\large\rm f(g)=\frac{7}{x^2}+10\]

Answer 13

ohh okay cool. So, should I put that as my answer or what do you think I should put?

Answer 14

Let \(\large\rm f(x)=\frac{7}{x}+10\) and \(\large\rm g(x)=x^2\).

Taking the composition f of g of x gives us,
\(\large\rm f(g(x))=\frac{7}{x^2}+10\)

You could say something like that I suppose ^
I like to use that lazy shortcut notation, leaving out the (x) in the function notation but your teacher probably won't like that. So it's best to do it this way.

Answer 15

awesomesauce thank you once again!