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I have this homework problem about functions. The goal is to find a function of form $$ f(x)=a+bc^{x}, c > 0 $$ $$ and $$ $$ f(0) = 15, f(2)=30, f(4)=90 $$ and then to find the domain of a another function called g(x) where $$ g(x) = ln(x), x = f(x) $$.

For the first part of the problem, to find a function of form, I created a system of thee equations $$ \begin{cases} a+bc^0=15\\ a+bc^2=30\\ a+bc^4=90 \end{cases} $$ And this is where I got stuck. I don't know how to solve this system. Any help will be appreciated.

letsgooo
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1 Answers1

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Subtract the first equation from the second $$ \tag{1}b(c^2 - 1) = 15$$ Subtract the second equation from the third $$ \tag{2} b(c^4 - c^2) = bc^2(c^2 - 1) = 60$$ Divide $(2)$ by $(1)$ $$ c^2 = 4$$ It's pretty straightforward from here on.

Ankit Saha
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