MHB What Is the Value of f(2) if f(x) = a^x and f(3) = 64?

[goosey00]

If you have f(x)=a^x and f(3)=64 what does f(2)=? Am I over thinking this one? Is it just f(2)=64 also?

 

[SuperSonic4]

Re: solve for f(x)a^x

If you have f(x)=a^x and f(3)=64 what does f(2)=? Am I over thinking this one? Is it just f(2)=64 also?

f(b) means evaluate f(x) at the value b. In this case f(3) means find f(x) when x=3.

Since you have the constant $a$ you can find it's value from f(3) [64 is a cube number so $a$ is a whole number] as an intermediate step. You won't need a calculator for this one but as a hint $64 = 4^3$

1. Solve $f(3)$ in terms of $a$ by substituting $x=3$ in $f(x)=a^x$
2. Work out the value of $a$ from the above since you're told that f(3) = 64
3. Use that value of $a$ to find $f(2) $ by substituting $x=2$

 

[goosey00]

Re: solve for f(x)a^x

So it would be 4^2 so f(2)=16? right?

 

[MarkFL]

Re: solve for f(x)a^x

Yes, since:

$\displaystyle a^3=4^3\,\therefore\,a=4\,\therefore\,f(x)=4^x\, \therefore\,f(2)=4^2=16$

 

[HallsofIvy]

Re: solve for f(x)a^x

An equivalent way to do this would be to note that a^2= (a^3)^{2/3}= 64^{2/3}.