Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. (2 points)

f(x) = 4/x and g(x) = 4/x

Answer 1

I think it might be
f(g(x)) = f(4/x) = 8/x^2 = x
f(f(x)) = g(4/x) = 8/x^2 = x

but I am not sure.

Answer 2

So plug in f(x) into x from g(x): \(g( f(x) )\), which will get you from \(g(x) = \dfrac{4}{x}\) to \(g(f(x)) = \dfrac{4}{~\dfrac{4}{x}~}\)

Answer 3

So the answer is 4/4/x = x

Answer 4

Or no?

Answer 5

You could show that \(\dfrac{4}{~\dfrac{4}{x}~} = \dfrac{4x}{4}=x\).

Do same for \(f(g(x))\)

Answer 6

Ok, I will, even though I dont understand it. Thank you

Answer 7

What don't you understand?

Answer 8

Why there are two 4s?

Answer 9

Because both \(f(x)\) and \(g(x)\) are equal to \(\dfrac{4}{x}\), right?

So you have \(g(\mathbf{\color{red}{x}}) = \dfrac{4}{\mathbf{\color{red}{x}}}\Longrightarrow g(\mathbf{\color{red}{f(x)}}) = \dfrac{4}{\mathbf{\color{red}{\dfrac{4}{x}}}}\)

Does that make sense? Color helps?

Answer 10

Basically, you just replace x to f(x) aka 4/x

Answer 11

Ok thank you.