For equation y=(1/3)^x does it have an inverse? When I try to find the inverse, should I switch 1/3 into a decimal and then do x=(0.33333)^y and solve?

Question

3mar · Answer

May I help?

3mar · Answer

To get the inverse of any function f(x):
- Solve for x, i.e separate x in one side and the other terms in the other side, included f(x).
- Swap x and f(x).
- The result is the inverse of the original function.

rileystevens · Answer

Yes please, I'm trying to get an assignment done and I have to find the inverse of $$y=5^{x} $$ which I thought would be $$x=5^{y} $$ but when I substitute x for a negative number to graph I don't think you can solve $$-5=5^{y}$$. And then for $$y=\frac{ 1 }{ 3 }^{x} $$ I'm not sure if it would be $$x=\frac{ 1 }{ 3 }$$ and if that would make it $$x=(0.333333..)^{y}$$

3mar · Answer

Great job!
With my pleasure!

3mar · Answer

Can you follow my steps and tell me what you got?

3mar · Answer

@rileystevens

rileystevens · Answer

Perfect

triciaal · Answer

from above.
" but when I substitute x for a negative number to graph I don't think you can solve 
−5=5y"
need to solve for y = 
the graph is y as a function of x

rileystevens · Answer

so would it be $$\frac{ -5 }{ 5 }=\frac{ 5y }{ 5 }$$ -1=y

danjs · Answer

$$\large y=5^x$$

For that function, think about what happens as you start putting in larger and larger negative numbers for x. The y value becomes smaller and smaller approaching zero but never getting there. The graph is...
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