functions

[xc630]

Hi I need help with this problem. For the exponential function f (x)=ab^x,
f(2)= 2 and f(4)=18

I need to find a & b. How would I do this?

 

[pka]

From the given you know that: ab<SUP>2</SUP>=2 & ab<SUP>4</SUP>=18.
Can you finish it? Hint: DIVIDE!

 

[xc630]

ok I got b= 3 and a=2/9

the 2nd part of the question asks what is f^-1(54). how would I do this?

 

[pka]

Because 9=3<SUP>2</SUP>, a=2/(3<SUP>2</SUP>).
Thus we rewrite the function as f(x)=2(3<SUP>x−2</SUP>).
To do your other question, solve 2(3<SUP>x−2</SUP>)=54 for x.

 

[xc630]

I don't understand how you rwrote the function.

 

[pka]

Well, we have 3<SUP>x</SUP>/3<SUP>2</SUP>=3<SUP>x−2</SUP>.
Simply subtract exponents.