Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x.

f of x equals four divided by x. and g of x equals four divided by x

Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. 

f of x equals four divided by x.  and g of x equals four divided by x

destinykiara99 · Answer

@hero @Jaynator495

satellite73 · Answer

$$f(g(x))=f(\frac{4}{x})$$ is a start

satellite73 · Answer

then since $$f(\diamondsuit)=\frac{4}{\diamondsuit}$$
you have $$f(\frac{4}{x})=\frac{4}{\frac{4}{x}}$$ and then a little algebra

destinykiara99 · Answer

Okay, where do you go from there??
I'm sorry, Pre-Calc is very confusing to me and I don't fully understand the lesson.

destinykiara99 · Answer

@satellite73

satellite73 · Answer

multiply by the reciprocal $$\frac{4}{\frac{4}{x}}=4\times \frac{x}{4}=x$$

satellite73 · Answer

just like $$\frac{4}{\frac{4}{5}}=4\times \frac{5}{4}=5$$

destinykiara99 · Answer

That makes sense :)

skullpatrol · Answer

Recall a variable is a symbol used to represent one or more numbers. 

So that means you can treat them as numbers and use all the operations you have been doing with numbers on them.