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- Oct 9th 2012, 09:51 AMEraser147Formula for f of g
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- Oct 9th 2012, 10:09 AMPlatoRe: Formula for f of g
- Oct 9th 2012, 10:31 AMEraser147Re: Formula for f of g
Yes, but going from there, I don't know how to find the x. It's just too confusing from there. I don't know which exponent I can factor out.

- Oct 9th 2012, 10:34 AMalane1994Re: Formula for f of g
Plato is correct. If you want f of g, you just plug the g function into the x spot on the f function.

$\displaystyle f=number^x$

$\displaystyle g=blahx$

then $\displaystyle f\circ g(x)=number^{blahx}$

Does this make sense?

If I am incorrect on this please correct me!:) - Oct 9th 2012, 10:40 AMPlatoRe: Formula for f of g
- Oct 9th 2012, 10:54 AMSorobanRe: Formula for f of g
Hello, Eraser147!

Quote:

$\displaystyle \text{Given: }\begin{Bmatrix}f(x) &=& 7^{2+5x} \\ g(x) &=& \log_7(x) \end{Bmatrix} \quad \text{ Find }f\!\!\circ\! g.$

$\displaystyle f\!\!\circ\!g \;=\;f(g(x))$

. . . $\displaystyle =\;f(\log_7x)$

. . . $\displaystyle =\;7^{2+5\log_7(x)}$

. . . $\displaystyle =\;7^2\cdot 7^{5\log_7(x)} $

. . . $\displaystyle =\;49\cdot 7^{\log_7(x^5)} $

. . . $\displaystyle =\;49\cdot x^5$

. . . $\displaystyle =\;49x^5$

- Oct 9th 2012, 11:16 AMEraser147Re: Formula for f of g
^ Thankyou that made more sense. I had to separate the 7s.

- Oct 9th 2012, 11:43 AMEraser147Re: Formula for f of g
Just one more question, can someone explain why when 7 is extended to the power of log 7 and raised to the x^5, why does it cancel and equate to x^5?

- Oct 9th 2012, 12:00 PMPlatoRe: Formula for f of g
- Oct 9th 2012, 12:25 PMEraser147Re: Formula for f of g
Thanks

- Oct 9th 2012, 12:30 PMHallsofIvyRe: Formula for f of g
That is, pretty much, the

**definition**of "$\displaystyle log_a(x)$"- it is the inverse function to $\displaystyle a^x$: $\displaystyle a^{log_a(x)}= log_a(a^x)= x$.